# If X= 3 + Sqrt8, Find the Value of X^2 + 1/X^2 - Mathematics

if   x= 3 + sqrt8, find the value of x^2 + 1/x^2

#### Solution

We know that x^2 + 1/x^2 = (x +1/x)^2 - 2. We have to find the value of x^2 + 1/x^2. As x = 3 + sqrt8

therefore

1/x = 1/(3 + sqrt8)

We know that rationalization factor for 3 + sqrt8 is 3 - sqrt8. We will multiply numerator and denominator of the given expression 1/(3 = sqrt8) by 3 - sqrt3 to get

1/x = 1/(3 +  sqrt8) xx (3 - sqrt8)/(3 -sqrt8)

= (3 - sqrt8)/(9 - 8)

= 3 - sqrt8

Putting the vlaue  of x and 1/x, we get

x^2 + 1/x^2 = (3 + sqrt8 + 3 - sqrt8)^2 - 2

= (6)^2 - 2

= 36 - 2

= 34

Hence the given expression is simplified to 34.

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 11 | Page 15

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