HOW MUCH EASY IS THIS ???

Algebra Level 3

If x^2+y^2=7 and x^3+y^3=10,then find the value of x+y?

9/2 5 6 4

Mridul Khare by Mridul KHARE , 21, India

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2 solutions

Let x + y = a x+y=a & x y = b xy=b .

Then a 2 − 2 b = 7 a^{2}-2b=7 & a 3 − 3 a b = 10 a^{3}-3ab=10 .

Eliminating b b using both equation, we have a 3 − 21 a + 20 = 0 a^{3}-21a+20=0

or ( a − 1 ) ( a + 5 ) ( a − 4 ) = 0 (a-1)(a+5)(a-4)=0

Hence a = a= 1 or 4 or -5. And out of these only one is in the given choices. So I guess there is nothing wrong in the question and the choices.

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i doubt the options are wrong! answer should be 1 as either of abscissa or the ordinate is negative but here answer goes for |x|+|y|=4

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