Question

Given that x²+ y² = 20 and xy = 7, calculate (x - y)².​

Answer 1

Answer: (x - y)² = 6

Concept:

Here, we need to know the concept of FOIL.

It is a way to expand squared or greater exponents parenthesis.

• F irst
• O uter
• I nner
• L ast

Explanation:

Given information

x² + y² = 20

xy = 7

Given expression

(x - y)²

Expand parenthesis through FOIL

= (x - y) (x - y)

= x · x - x · y - x · y + y · y

= x² - 2xy + y²

Substitute values into the expression

= x² + y² - 2xy

= (20) - 2 (7)

= 20 - 14

=
`\boxed{6}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

6

Explanation:

`Here,\\\\\hookrightarrow x^(2) +y^(2) =20\:and\:xy=7\\\\Now,\\\\\hookrightarrow (x - y)^(2) \\\\Applying\:formula\\\\\hookrightarrow (x-y)^(2) =x^(2) -2xy+y^(2) \\\\Then\: we\: get\\\\\hookrightarrow x^(2) -2xy+y^(2) \\\\\hookrightarrow x^(2) +y^(2) -2xy\\\\\hookrightarrow 20-(2*7)[Because\:x^(2) +y^(2) =20\:and\:xy=7]\\\\\hookrightarrow 20-14\\\\\hookrightarrow 6`