Question

If $x-y=8,xy=2$, find $x^2+y^2$.

• A. 66
• B. 81
• C. 68
• D. 72

Answer 1

Answer: (C)

68

$x-y=8\Rightarrow x=y+\mathrm{8.........}\left(1\right)$

Now, $xy=2\Rightarrow y(y+8)=2\Rightarrow y^2+8y-2=\mathrm{0.......}\left(2\right)$

Now, Squaring (1)

$x^2=y^2+16y+64\Rightarrow 8y=\frac{x^2-y^2-64}{2}........\left(3\right)$

From (2) and (3)

$y^2+\frac{x^2-y^2-64}{2}-2=0\Rightarrow \frac{x^2+y^2}{2}-32-2=0\Rightarrow \frac{x^2+y^2}{2}=34\Rightarrow x^2+y^2=68$