Question

If x =√5 + 2 then find value of x-1/x​

Answer 1

Step-by-step explanation:

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Answer 2

Solution:

Given:

$x = \sqrt{5} + 2$

Now,By rationalizing the denominator,we get:

$\frac{1}{x} = \frac{1}{ \sqrt{5} + 2} = \frac{1}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 } = \frac{ \sqrt{5} - 2}{ \sqrt5{}^{2} - 2 {}^{2} } = \sqrt{5} - 2$

$x - \frac{1}{x} = \sqrt{5} +2 - ( \sqrt{5} - 2) = \sqrt{5} + 2 - \sqrt{5} + 2 = 4$

The answer is 4.

Rationalising:

It is a process by which the roots in the denominator are eliminated.

Rationalising factor:

A term which is multiplied to make the number a rational.

For example,

1/√7=1/√7×√7/√7=√7/7

Here,√7/√7 is the rationalising factor