If x^2 + x = 5 then the value of (x+3)^3 + 1/(x+3)^3 is :

SSC CGL 16 Aug 2015 Shift 2 Paper

Question : 121 of 200

Marks: +1, -0

x^2

+ x = 5 then the value of

(x+3)^3 + 1/(x+3)^3

is :

Solution:

x^2

+ x = 5 (Given)
Let, x + 3 = a
∴

1/{x+3}

1/a

Now,
a +

1/a

= (x + 3) +

1/(x-3)

{(x+3)^2+1}/{x+3}

{x^2+6x+9+1}/{x+3}

{x^2+6x+10}/{x+3}

{x^2+x+5x+10}/{x+3}

{5+5x+10}/{x+3}

{5x+15}/{x+3}

{5(x+3)}/{x+3}

= 5
∴

a^3+1/x^3

(a+1/a)^3

- 3a ×

1/a (a+1/a)

(5)^3

- 3 × 5 = 125 - 15 = 110

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