SSC CGL 30 Aug 2015 Paper

© examsiri.com

Question : 112 of 200

Marks: +1, -0

If x =

{√3+√2}/{√3-√2}

, then

x^3+1/x^3

is equal to

98
100
5
970

Solution:

x =

{√3+√2}/{√3-√2}

=

{(√3+√2)(√3+√2)}/{(√3-√2)(√3+√2)}

(Rationalising the denominator)
=

(√3+√2)^2/{(√3)^2-(√2)^2}

=

{3+2+2√6}/{3-2}

= 5 + 2

√6

∴

1/x

=

1/{5+2√6}

=

(5-2√6)/{(5+2√6)(5-2√6)}

=

(5-2√6)/{(5+2√6)(5-2√6)}

=

{5-2√6}/{25-24}

= 5 -

2√6

∴ x +

1/x

= 5 + 2

√6

+ 5 - 2

√6

= 10
∴

x^3+1/x^3

=

(x+1/x)^3

- 3x ×

1/x(x+1/x)

=

(10)^3

- 3 × 10
= 1000 – 30 = 970

© examsiri.com

Go to Question:

Prev Question

Next Question