Generate Pythagorean Triples using an identity You'll gain access to interventions, extensions, task implementation guides, and more for this instructional video In this lesson you will learn to generate a Pythagorean Triple by using the identity (x^2 y^2)^2 (2xy)^2 = (x^2 y^2)^2The problem above requires us to do two things First, generate a Pythagorean Triple using the integers 3 and 5Second, we need to figure out if the generated triple is Primitive or ImprimitiveFind an answer to your question find the identity of x^2y^2 =?
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The identity (x^2 y^2)^2=(x^2-y^2)^2 (2xy)^2 can be used to generate pythagorean triples
The identity (x^2 y^2)^2=(x^2-y^2)^2 (2xy)^2 can be used to generate pythagorean triples-👍 Correct answer to the question The identity (x^2y^2)^2 = (x^2y^2)^2 (2xy)^2 can be used to generate pythagorean triples what pythagorean triple could be generated using x=8 and y=3 ehomeworkhelpercomThe Pythagorean triple Identity is (x 2 y 2) 2 = (x 2 y 2) 2 (2xy) 2, where c = x 2 y 2, a = x 2 y 2, and b = 2xy With x = 3 and y = 5 a = 3 2 5 2 = 16, (this is 16, by the rules x should be greater than y (x > y), in this case √(x 2 y 2) 2 = a) b = 2*3*5 = 30 c = 3 2 5 2
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X and y are positive integers;Use the Pythagorean identity, (x^2y^2) (2xy)^2 = (x^2y^2)^2 , to create a Pythagorean triple Follow these steps 1 Choose two numbers and identify which is replacing x and which is replacing y 2 How did you know which number to use for x and for y?👍 Correct answer to the question Use the identity (x^2y^2)^2=(x^2−y^2)^2(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6 eeduanswerscom
The identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean The identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be generated using x = 8 and y = 3?Correct answers 2 question The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triplePlease help Thanks in advance We have x2=2xy 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 2xy 3y2 = 0 ?
HSAAPRC4 Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triplesX2 y2 can be written as (xy)2 this is in the form of (a b)2 = a2 2ab b2so the above can be written as x2 2xy y2or there is another one too x2 y2 =For example, the polynomial identity (x 2 y 2) 2 = (x 2 – y 2) 2 (2xy) 2 can be used to generate Pythagorean triples Suggested Learning Targets Understand that polynomial identities include but are not limited to the product of the sum and difference of two terms, the difference of two squares, the sum and difference of two cubes, the
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Example 2 Use the integers 3 and 5 to generate a Pythagorean Triple Is the generated triple a Primitive or Imprimitive Pythagorean Triple? Correction (after missing a sign) As kobe pointed out, the original DE is $$ (x^2y^2)y'2xy=0, $$ which as equation for a vector field reads $$ (x^2y^2)\,dy2xy\,dx=0\iff Im(\bar z^2\,dz)=0\text{ with } z=xiy $$ From the complex interpretation it is directly visible that this is not integrable, for that it would have to be an expression Saikiran Reddy and Kwasi F give excellent solutions to this The answer, dy/dx =1 might make us think about the question a bit For x^2y^2=2xy, we get (by differentiating implicitly), dy/dx =1 That's the same as the derivative of a linear function with slope, 1 Hmmmmm Let's see If we have x^2y^2=2xy The we must also have x^22xy y^2=0 Factoring gets us (xy)^2
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Satyajeetdamekar004 satyajeetdamekar004 Math Secondary School answeredStudents will prove the polynomial identity ( x^2 y^2 )^2 ( 2xy )^2 = ( x^2 y^2 )^2 and use it to generate Pythagorean triplesUse this activity as independent/partner practice or implement it as guided notes and practice for students in need ofCCSSMathContentHSAAPRC4 Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x 2 y 2) 2 = (x 2 y 2) 2 (2xy) 2 can be used to generate Pythagorean triples Authors National Governors Association Center for Best Practices, Council of Chief State School Officers
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Use the identity (x^2y^2)^2=(x^2−y^2)^2(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6Further remarks May 6 The polynomial ring $\mathbb{H}u$ has a natural division ring of fractions, $\mathbb{H}(u)$, which is isomorphic to a certain ring of $2 \times 2$ matrices over $\mathbb{C}(u)$ (I can't get the latex right for matrices, but the ring should be clear in particular, the determinants of elements in the ring are elements of $\mathbb{R}(u)$)Find dy/dx x^2y^2=2xy Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate Tap for more steps By the Sum Rule, the derivative of with respect to is Differentiate using the Power Rule which states that is where
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Marshall uses the polynomial identity (x?y)^2=x^2?2xyy^2 to show that 8 = 64 What values can Marshall use for x and y?Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity $(x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2$ can be used to generate Pythagorean triplesSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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Determine the dimensions of the squares that must be cut to create a box with Calculus The line that is normal to the curve x^2=2xy3y^2=0 at(1,1) intersects the curve at what other point? Answer 2 📌📌📌 question The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be generated using x = 8 and y = 3?Correct answers 2 🔴 question Type the correct answer in each box In part E, you proved that any Pythagorean triple can be generated using the identity (x^2 − y^2)^2 (2xy)^2 = (x^2 y^2)^2 Find the missing x and yvalues and Pythagorean triples using the identity given Write the triple in parentheses, without spaces between the values, with a comma between values, and in order
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Answer 2 📌📌📌 question The identity (x^2y^2)^2 = (x^2y^2)^2 (2xy)^2 can be used to generate pythagorean triples what pythagorean triple could be generated using x=8 and y=3 the answers to estudyassistantcom3 Explain how to find a Pythagorean triple using those numbers 4Use the Pythagorean identity, Latex (x^2y^2)^2(2xy)^2=(x^2y^2)^2\textsf{,} to create a Pythagorean triple Follow these steps Choose two numbers and identify which is replacing
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Theorem The positive primitive solutions of x^2 y^2 = z^2 with y even are x = r^2 s^2, y = 2rs, z = r^2 s^2, where r and s are arbitrary integers of opposite parity with r>s>0 and gcd(r,s)=1 Using this theorem, find all solutions of the equation x^2 y^2 = 2z^2 (hint write theCalculus Find two numbers whose sum is 10 for which the sum of their squares is a minimum algebra The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2y2 represent the lengths of three sides of a right triangle;Add − x 2 y 2 x 2 y 2 and x 2 y 2 x 2 y 2 Add x 2 x 2 x 2 x 2 and 0 0 Simplify each term Tap for more steps Multiply x 2 x 2 by x 2 x 2 by adding the exponents Tap for more steps Use the power rule a m a n = a m n a m a n = a m n to combine exponents Add 2 2 and 2 2
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HSAAPRC4 Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x 2 y 2 ) 2 = (x 2 y 2 ) 2 (2xy) 2 can be used to generate Pythagorean triplesExtended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music The identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be generated using x = 8 and y
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Correct answers 2 question Use the identity (x^2y^2)^2=(x^2−y^2)^2(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6The answers to estudyassistantcom👍 Correct answer to the question Use the identity (x^2y^2)^2=(x^2−y^2)^2(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6 ehomeworkhelperscom
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