If x^2 + y^2 = 25, ;xy = 12, then x = - Vidyadip

MCQ

If ${x^2} + {y^2} = 25,\;xy = 12$, then $x = $

A
$\{3, 4\}$
B
$\{3, -3\}$
✓
$\{3, 4, -3, -4\}$
D
$\{-3, -3\}$

✓

Answer

Correct option: C.

$\{3, 4, -3, -4\}$

c
(c) ${x^2} + {y^2} = 25$ and $xy = 12$

==> ${x^2} + {\left( {\frac{{12}}{x}} \right)^2} = 25\,\,$

$\Rightarrow {x^4} + 144 - 25{x^2} = 0$

==> $({x^2} - 16)({x^2} - 9) = 0$

==> ${x^2} = 16$ and ${x^2} = 9$

==> $x = \pm \,4$ and $x = \pm 3$.

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