The square-root of (0.75)^3/{1-(0.75)}+(0.75+(0.75)^2+1) is

KVPY SA Exam 2012 Question Paper

Question : 2 of 80

Marks: +1, -0

The square-root of

(0.75)^3/{1-(0.75)}+(0.75+(0.75)^2+1)

Solution:

Say 0.75 is x
then

x^3/{1-x}+(x^2+x+1)=P

{x^3-(x-1)(x^2+x+1)}/{1-x}=P

{x^3-x^3+1}/{1-x}=P

⇒1/{1-x}=P

⇒P=1/{1-3/4}=4/1

∴√P=2

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