Question

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Find the missing X- and y-values and Pythagorean triples using the identity

(x? y?)2 + (2xy)2 = (x² + y2)2.

Write the triples in parentheses with commas but no spaces between the values, and order the values

from least to greatest.

Type the correct answer in each box.

Answer 1

Question:

Find the missing x- and y-values and Pythagorean triples using the identity given

$(x\²-y\²)\² + (2xy)\² = (x\²+y\²)\²$

$x = 4$

$y = 3$

Pythagorean Triples:

Write the triples in parentheses with commas but no spaces between the values, and order the values  from least to greatest.

Answer:

Pythagorean triples is: (7, 24, 25)

Step-by-step explanation:

Pythagorean triples is expressed as:

$a^2 + b^2 = c^2$

In $(x\²-y\²)\² + (2xy)\² = (x\²+y\²)\²$

$a^2= (x^2 -y^2)^2$

Take square root of both sides

$a = x^2 - y^2$

$b^2 = (2xy)^2$

Take square root of both sides

$b = 2xy$

$c^2 = (x^2 + y^2)^2$

Take square root of both sides

$c = x^2 + y^2$

So, we have:

$x = 4$

$y = 3$

Pythagorean Triples: ?

$a = x^2 - y^2$

$a = 4^2 - 3^2$

$a = 16 - 9$

$a = 7$

$b = 2xy$

$b = 2 * 4 * 3$

$b = 24$

$c = x^2 + y^2$

$c = 4^2 + 3^2$

$c = 16 + 9$

$c= 25$

Hence, the Pythagorean triples is: (7, 24, 25)