Question

Please explain with proper written steps

Answer 1

9

Step-by-step explanation:

Given:

$\sqrt{x + 16} - \sqrt{x} = 2$

To find:

The value of x

Solution:

$\sqrt{x + 16} - \sqrt{x} = 2 \\ \\ \sqrt{x + 16} - 2 = \sqrt{x} \\ \\ \text{[Squaring both side]} \\ \\ {( \sqrt{x + 16} - 2) }^{2} = {( \sqrt{x}) }^{2} \\ \\ {( \sqrt{x + 16}) }^{2} + {(2)}^{2} - 2.2. \sqrt{x + 16} = x \\ \\ x + 16 + 4 - 4 \sqrt{x+16} = x \\ \\\cancel{x} + 20 - 4 \sqrt{x+ 16}=\cancel{x}\\\\ 20 = 4 \sqrt{x+16} \\ \\\cancel{20} = \cancel{4} \sqrt{x + 16} \\ \\ 5 = \sqrt{x + 16} \\ \\ \text{[Squaring both side]} \\ \\ {(5)}^{2} = {( \sqrt{x + 16}) }^{2} \\ \\ 25 = x + 16 \\ \\ 25 - 16 = x\\ \\ x = 9$

Therefore, The required value of x is 9.

Important Formula

${x}^{2}+{y}^{2}+2xy={(x + y)}^{2}\\\\{x}^{2}+{y}^{2}-2xy={(x - y)}^{2}\\\\(x + y)(x - y)={x}^{2}-{y}^{2}$