5^2 + 12^2 = 13^2
That is, x^2 + y^2 = 13
Use the identity (x^2+y^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.
Is it 169?
2 answers
The difference of the squares of the numbers is 5 mean:
x² - y² = 5
The product of the numbers is 6 mean:
x ∙ y = 6
Replace this values in equation:
( x² + y² )² = ( x² − y² )² + ( 2 x y )²
( x² + y² )² = 5² + ( 2 ∙ 6 )²
( x² + y² )² = 25 + 12²
( x² + y² )² = 25 + 144
( x² + y² )² = 169
Take square root of both sides:
x² + y² = √169
x² + y² = 13
x² - y² = 5
The product of the numbers is 6 mean:
x ∙ y = 6
Replace this values in equation:
( x² + y² )² = ( x² − y² )² + ( 2 x y )²
( x² + y² )² = 5² + ( 2 ∙ 6 )²
( x² + y² )² = 25 + 12²
( x² + y² )² = 25 + 144
( x² + y² )² = 169
Take square root of both sides:
x² + y² = √169
x² + y² = 13
1 answer