Question

If ${(x+y)}^2=144$ and $x^2-y^2=24$, then what is $x$ if $x$ and $y$ are both positive?

• A. $7$
• B. $5$
• C. $12$
• D. $2$
• E. $8$

Answer 1

Answer: (A)

$7$

$(x+y{)}^2=144$ ....Given

Taking square roots o both sides, we get

$x+y=12$ ...(1) ....Since $x$ & $y$ are both positive

$x^2-y^2=24$ ....Given

$(x+y)(x-y)=24$

$\therefore x-y=2$ ...(2)

Adding eq(1) and eq(2), we get

$2x=14\Rightarrow x=7$