Question

If x=3-2√2,find the value of x^2+1/x^2
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Answer 1

Solution:

i ) x = 3-2√2 ----(1)

ii ) 1/x = 1/(3-2√2)

Rationalising the denominator, we get

= (3+2√2)/[(3-2√2)(3+2√2)]

= (3+2√2)/[3² - (2√2)²]

= (3+2√2)/[9-8]

= 3+2√2 -----(2)

iii ) x + 1/x

= 3-2√2+3+2√2

= 6 ----(3)

Now ,

x²+1/x²

= (x+1/x)²-2

= 6² - 2

= 36 - 2

= 34

Therefore,

x²+1/x² = 34

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