Question

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

• A. 0
• B. 106
• C. 14
• D. 52

Answer 1

The correct option is A

0

2($x^2$ + $y^2+2xy)-5(x^2$ - 2xy + $y^2$)
= 2$x^2$ +2$y^2$ + 4xy - 5$x^2$ + 10xy - 5$y^2$
= -3$x^2$ - 3$y^2$ + 14xy
= -3($x^2+y^2$) + 14xy
= (-3 $\times$ 14) + (14 $\times$ 3)
= - 42 + 42
= 0