Question

Given that x^2+y^2=9 and xy=5, find the value of (x - y)^2. ​

Answer 1

`(x -y)^2 = -1`

Explanation:

`(x - y)^2 = x^2 + y^2 - 2xy`

`= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1`

Answer 2

The binomial expansion of (x - y)² is

(x - y)² = x² - 2xy + y²

Substitute the given values to the equation

(x - y)² = x² - 2xy + y²

(x - y)² = x² + y² - 2xy

(x - y)² = 9 - 2(5)

(x - y)² = 9 - 10

(x - y)² = -1

Therefore the value of (x - y)² is -1.

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