Question

Plzz help me with this. ​

Answer 1

$x = 9 + 4 \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{9 + 4 \sqrt{5} } \\ \\ = \frac{9 - 4 \sqrt{5} }{81 - 80} \\ \\ = 9 - 4 \sqrt{5} \\ \\ \\ x + \frac{1}{x} = 9 + 4 \sqrt{5} + 9 - 4 \sqrt{5} = 18 \\ \\ \\ now \\ \\ {( \sqrt{x} - \frac{1}{ \sqrt{x} }) }^{2} = x + \frac{1}{x} - 2 \sqrt{x} \times \frac{1}{ \sqrt{x} } \\ \\ {( \sqrt{x} - \frac{1}{ \sqrt{x} }) }^{2} =18 - 2 = 16 \\ \\ \sqrt{x} - \frac{1}{ \sqrt{x} } = \sqrt{16} = \pm4$


KEY POINTS TO REMEMBER :-

☸️ Rationalizing the terms :- It is by making the denominator a rational number.

☸️ When square is transposed to the other side of the equation, Then it becomes Plus-Minus under root.

☸️ (a+b) ²=a² + b² + 2ab

☸️ (a-b) ²= a² + b² - 2ab


Thanks!

Answer 2

answer is not + - 4.

it's 4.

let take example

value of √x²=x

but value of x is + -4.