If x=5-2√6.

Find value of √x-1/√x.

Open in App

Solution

x=5-2√6
=3+2-2√3√2
=(√3)²-2√3√2+(√2)²
=(√3-√2)²
∴, √x=√3-√2
∴, 1/√x
=1/√3-√2
=(√3+√2)/(√3-√2)(√3+√2)
=(√3+√2)/{(√3)²-(√2)}
=(√3+√2)/(3-2)
=√3+√2
∴, √x-1/√x
=√3-√2-√3-√2
=-2√2

Suggest Corrections

Similar questions

x

\frac{x + 1}{2} - \frac{x + 2}{5} = \frac{x - 1}{2}

x

5^{x} + 5^{x + 1} + 5^{x + 2} = 775

x + \frac{1}{x} = 2

x^{5} + \frac{1}{x^{5}}

If \x+\frac{1}{x}1/x = 5\), then the value of $\frac{3 x^{2} + 3}{2 x^{2} + 5 x + 2}$ = ?

Join BYJU'S Learning Program