Question

If $x^2$ + $y^2$ = 14 and $xy=3$, the value of

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

• A. 0.0
• B. 52
• C. 106
• D. 14

Answer 1

The correct option is A 0.0

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

= $2(x^2$ + $y^2+2xy)-5(x^2$ - $2xy$ + $y^2$)
= $2x^2+2y^2+4xy-5x^2+10xy-5y^2$
= $-3x^2-3y^2+14xy$
= -3($x^2+y^2$) + $14xy$

On substituting $x^2$ + $y^2$ = 14 and $xy=3$, we get
= $(-3\times 14)+(14\times 3)$
= - 42 + 42
= 0