Question

If a=3-2√2, then find the value of ( a^2 + 1÷ a^2)

Answer 1

Solution:

i) a = 3-2√2 ----(1)

ii) 1/a = 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) a + 1/a = 3-2√2+3+2√2=6

Now ,

a²+1/a²

= (a+1/a)² - 2

= 6² - 2

= 36 - 2

= 34

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