KVPY SA Exam 2013 Question Paper

Question : 5 of 80

Marks: +1, -0

Let x,y,z be non-zero real numbers such that

x/y+y/z+z/x=7

and

y/x+z/y+x/z=9

then

x^3/y^3+y^3/z^3+z^3/x^3-3

is equal to

Solution:

a^3 + b^3 + c^3 - 3abc

= [a + b + c] [(a + b + c) ^2

- 3(ab + bc + ca)]

= [7] [(7)^2 -3(9)]

= 7(49 - 27) = 7 × 22 = 154

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