Question

If $x^2$ + $y^2$ = 28 and xy = 6, find the value of 4${(x+y)}^2$ - 10${(x-y)}^2$.

• A. 336
• B. -168
• C. 168
• D. 0.0

Answer 1

The correct option is D 0.0

Given:$4(x+y{)}^2-10(x-y{)}^2$.

Using identities,
$(a+b{)}^2=a^2+2ab+b^2$
$(a-b{)}^2=a^2-2ab+b^2$,we have

4($x^2$ + $y^2+2xy)-10(x^2$ - $2xy$ + $y^2$)
= 4$x^2$ +4$y^2$ + $8xy$ - 10$x^2$ + $20xy-10$$y^2$
= -6$x^2$ - 6$y^2$ + $28xy$
= -6($x^2+y^2$) + $28xy$
= (-6 $\times$ 28) + (28 $\times$ 6)
= - 168 + 168
= 0