Question

Solve the following equations for $(x+y)$
$\sqrt{x+y}+\sqrt{x-y}=4$, $x^2-y^2=9$

• A. $9$
• B. $2$
• C. $1$
• D. $10$

Answer 1

Answer: (A), (C)

The correct options are
A $9$
C $1$

$x^2-y^2=9$ ......(i)

$\sqrt{x+y}+\sqrt{x-y}=4$

Squaring both sides, we get

$x+y+x-y+2\sqrt{x+y}\sqrt{x-y}=16\Rightarrow 2x+2\sqrt{x^2-y^2}=16$

Substituting (i), we have
$2x+2\sqrt{9}=16\Rightarrow 2x=10\Rightarrow x=5$

Substituting $x$ in (i), we get

$5^2-y^2=9\Rightarrow y^2=16\Rightarrow y=\pm 4$