Question

If a= 3+2√2 find a^2+1/a^2

Answer 1

Solution:

Given

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 ----(3)

iv) a²+1/a²

= (a+/1a)²-2

= 6²-2

= 36 - 2

= 34

Therefore,

a²+1/a² = 34

••••

Answer 2

Answer:

Solution:

Given

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 ----(3)

iv) a²+1/a²

= (a+/1a)²-2

= 6²-2

= 36 - 2

= 34

Therefore,

a²+1/a² = 34

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