If x+y=12 and x y=27 then the value of x^3+y^3

Sainik School Entrance Exam 2019 Solved Paper

Question : 41 of 150

Marks: +1, -0

x+y=12

and

x y=27

then the value of

x^3+y^3

Solution:

(a)

x+y=12

and

x y=27

Squaring on both sides,

x^2+y^2+2 x y=144

x^2+y^2+2 ×27=144

x^2+y^2=90

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

=12 .(90-27)

=12 ×63=756 .

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