Question

wrong answer will be reported and deleted..solution wise answer will be marked brainliest​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

$\sqrt{x + 3} + \sqrt{x - 2} = 5$

Squaring both sides

${( \sqrt{x + 3} \: + \: \sqrt{x - 2} \: )}^{2} \: = {5}^{2}$

$\implies \: (x + 3) + (x - 2) + 2 \sqrt{(x + 3) \: (x - 2)} = 25$

$\implies \: (2x + 1) + 2 \sqrt{(x + 3) \: (x - 2)} = 25$

$\implies \: (2x - 24) = - 2 \sqrt{(x + 3) \: (x - 2)}$

$\implies \: (x - 12) = - \sqrt{(x + 3) \: (x - 2)}$

Again squaring both sides

${(x - 12)}^{2} = {( - \sqrt{(x + 3)(x - 2)} \: \: )}^{2}$

$\implies \: {x}^{2} - 24x + 144 = (x + 3)(x - 2)$

$\implies \: {x}^{2} - 24x + 144 = ( {x}^{2} + 3x - 2x - 6)$

$\implies \: {x}^{2} - 24x + 144 = ( {x}^{2} + x - 6)$

$\implies \: - 25x = - 150$

$\displaystyle \: \implies \: x \: = \frac{150}{25}$

$\therefore \: x \: = 6$

HENCE THE REQUIRED ANSWER IS x = 6

Answer 2

Step-by-step explanation:

$x = 6 \: ........................$