If $x^{2} + y^{2} = 14$ and $x y = 3$ , find the value of $2 {(x + y)}^{2} - 5 {(x - y)}^{2}$ .

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Solution

The correct option is A
0

$2 (x^{2} + y^{2} + 2 x y) - 5 x^{2} - 2 x y + y^{2})$

= $2 x^{2} + 2 y^{2} + 4 x y - 5 x^{2} + 10 x y - 5 y^{2}$

= $- 3 x^{2} - 3 y^{2} + 14 x y$

= $- 3 (x^{2} + y^{2}) + 14 x y$

= $(- 3 \times 14) + (14 \times 3)$

= $- 42 + 42$

= $0$

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Similar questions

If $x^{2}$ + $y^{2}$ = 14 and xy = 3, find the value of $2 {(x + y)}^{2} - 5 {(x - y)}^{2}$ .

If $x^{2} + y^{2} = 14$ and $x y = 3$ , find the value of $2 (x + y)^{2} - 5 (x - y)^{2}$ .

$If x^{2} + y^{2} = 14 and x y = 3,$
then find the value of
$2 (x + y)^{2} - 5 (x - y)^{2} .$

2 x + y = 14

x y = 6

4 x^{2} + y^{2}

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