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Algebra Level 1

If x and y are real numbers such that x+y=7 and x^3+y^3=133, find the value of xy.


The answer is 10.

Shashvat Jayakrishnan by Shashvat Jayakrishnan , 21, India

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3 solutions

Vishal S
Jan 2, 2015

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

By substituting the given values

We get

133=(7)(49-3xy)

=>19=49-3xy

=>30=3xy

=>xy=30/3

=>xy=10

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Krishna Garg
Aug 22, 2014

When we take cube on both sides of X+Y =7,and subsitute the given values we get 21xy =210 so xy =10 Ans K.K.GARG,India

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Solution:- x^3 + y^3= (x+y)^3 - 3xy(x+y) it is given x+y=7 putting value of it we get, 7^3-3xy(7)=133=x^3+y^3 343-133=21xy 210=21xy xy=10

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