If (3x – 2y) : (2x + 3y) = 5 : 6, then one of the values of ( {\sqrt^3 {x}+\sqrt^3{y}}/{\sqrt^3{x}-\sqrt^3{y}} )^{2} is

SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 18 of 100

Marks: +1, -0

(3x – 2y) : (2x + 3y) = 5 : 6

, then one of the values of

( {√^3 {x}+√^3{y}}/{√^3{x}-√^3{y}} )^{2}

Solution:

(3)

{3 x-2 y}/{2 x+3 y}= {5}/{6}

⇒ 18 x-12 y=10 x+15 y

⇒18 x-10 x=12 y+15 y

⇒ 8 x=27 y

⇒{x}/{y}= {27}/{8}

On taking cube root of both sides,

{√^3{x}}/{√^3{y}}=√^3{ {27}/{8}}= {3}/{2}

By componendo and dividendo,

{√^3 {x}+√^3{y}}/{√^3{x}-√^3{y}}

= {3+2}/{3-2}= {5}/{1}

On squaring both sides,

( {√^3 {x}+√^3{y}}/{√^3{x}-√^3{y}} )^{2}

= 5 × 5 = 25

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