Question

If $x^2+y^2=25,xy=12$,then complete set of x =

• A. {3, 4}
• B. {3, -3}
• C. {3, 4, -3, -4}
• D. {-3, -3}

Answer 1

The correct option is C

{3, 4, -3, -4}

$x^2+y^2=25$ and $xy=12$

⇒ $x^2+(\frac{12}{x}{)}^2=25$ ⇒ $x^4+144-25x^2=0$

⇒ $(x^2-16)(x^2-9)=0$ ⇒ $x^2=16$ and $x^2=9$

⇒ x= ±4 and x = ±3