Question

If x+y = 12 , xy= 14 find the value of x2-y2

Answer 1

x + y = 12. and xy = 14


( x + y )² = x² + 2xy + y²

(12)² = x² + y² + 2 × 14

144 = x² + y² + 28

x² + y² = 116




( x - y )² = x² - 2xy + y²


( x - y )² = 116 - 2 × 14


( x - y )²

Answer 2

using identity (a+b)^2=a^2-2ab+b^2
let a =x
b=y
$({x + y})^{2} = {x}^{2} + 2xy + {y}^{2} \\ {12}^{2} = {x}^{2} + {y}^{2} + 28 \\ 144 = {x}^{2} + {y}^{2} + 28 \\ {x}^{2} + {y}^{2} = 144 - 28 = 116$
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