Question

can anyone solve this??

Answer 1

Step-by-step explanation:

We have,

$\sqrt{3 - x} - \sqrt{x + 7} = \sqrt{x + 2}$

Squaring both sides,

$\implies3 - x + x + 7 - 2 \sqrt{(3 - x)(x + 7)} = x + 2$

$\implies10 - 2 \sqrt{(3 - x)(x + 7)} = x + 2$

$\implies8 - x = 2 \sqrt{(3 - x)(x + 7)}$

Squaring both sides,

$\implies64 + {x}^{2} - 16x = 4(3x + 21 - {x}^{2} - 7x)$

$\implies {x}^{2} - 16x + 64 = - 16x + 84 - 4 {x}^{2}$

$\implies5 {x}^{2} = 20$

$\implies {x}^{2} = 4$

$\implies \: x = 2 \: \: or \: \: x = - 2$