Question

solve the problem .

Answer 1

$\sqrt{x + 3} + \sqrt{x + 2} - \sqrt{2x + 4} > 0 \\ \sqrt{x + 3} + \sqrt{x + 2} - \sqrt{2} \sqrt{ x + 2} > 0 \\ \\ \sqrt{x + 3} - ( \sqrt{2} - 1) \sqrt{x + 2} > 0 \\ \sqrt{x + 3} > ( \sqrt{2} - 1) \sqrt{ x + 2} \\ squaring \: both \: sides \\ x + 3 > (2 + 1 - 2 \sqrt{2})(x + 2 ) \\ x + 3 > 3x - 2 \sqrt{2} x + 6 - 4 \sqrt{2} \\ 2 \sqrt{2} x - 2x > 3 - 4 \sqrt{2} \\ x(2 \sqrt{2} - 2) > 3 - 4 \sqrt{2} \\ x > \frac{3 - 4 \sqrt{2} }{2 \sqrt{2} - 2}$