SSC CGL 26 Oct 2014 Shift 1 Paper

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Question : 113 of 200

Marks: +1, -0

If 2x + 3y =

{11}/2

and xy =

5/6

, then the value of

8x^3+27y^3

is

583
${583}/4$
187
${671}/8$

Solution:

2x + 3y =

{11}/2

On cubing both sides,

(2x+3y)^3

=

({11}/2)^3

⇒

(2x)^3+(3y)^3

+ 3 . 2x . 3y (2x + 3y) =

{1331}/8

[

(a + b)^3

=

a^3 + b^3

+ 3ab (a + b)]
⇒

8x^3 + 27y^3

+ 18xy (2x + 3y)
=

{1331}/8

⇒

8x^3+27y^3

+ 18 ×

5/6 × {11}/2

=

{1331}/8

⇒

8x^3+27y^3

+

{165}/2

=

{1331}/8

⇒

8x^3+27y^3

=

{1331}/8-{165}/2

=

{1331-660}/{8}

=

{671}/8

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