If X= √ 2 − 1 , Then Write the Value of 1 X . - Mathematics

If x= $\sqrt{2} - 1$, then write the value of $\frac{1}{x} .$

Solution

Given that. x= sqrt2-1  Hence 1/xis given as

1/x = 1/(sqrt2-1)

We know that rationalization factor for sqrt2-1is sqrt2+1 . We will multiply each side of the given expression 1/(sqrt2-1)by, sqrt2+1 to get

1/(sqrt2-1) xx (sqrt2+1)/(sqrt2+1) = (sqrt2+1)/((sqrt2)^2 - (1)^2)

 = (sqrt2 +1)/(2-1)

= sqrt2 +1

Hence the value of the given expression issqrt2 +1.

Concept: Operations on Real Numbers
Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.3 | Q 5 | Page 16

Share