SSC CGL 26 Oct 2014 Shift 2 Paper

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Question : 126 of 200

Marks: +1, -0

The value of

(3+2√2)^{-3}

+

(3-2√2)^{-3}

is

198
180
108
189

Solution:

(3+2√2)

+

(3-2√2)

=

(3)^2 - (2√2)^2

= 9 - 8 = 1
∴ 3 +

2√2

=

1/{3-2√2}

(x + y)^3 + (x – y)^3

=

x^3 + y^3 + 3 x^2

y + 3 x

y^2 + y^3 + x^3 – y^3 – 3 x^2

y + 3 x

y^2

= 2

x^3

+ 6 x

y^2

∴

(3+2√2)^{-3}

+

(3-2√2)^{-3}

=

(1/{3+2√2})^3 + (1/{3-2√2})^3

=

(3-2√2)^{3}

+

(3+2√2)^{3}

= 2 ×

(3)^3

+ 6 × 3 ×

(2√2)^2

= 2 × 27 + 18 × 8
= 54 + 144 = 198

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