Problems with a a and b b , 1

Algebra Level 3

2 a 2 + 2 b 2 + a b a 3 + b 3 = 0 \dfrac {2a^{2}+2b^{2}+ab}{a^{3}+b^{3}} =0

The equation holds true for some a a and b b (not necessarily real) . Which of the options is correct?

a + b = 0 a+b=0 a = − 2 , b = 3 a=-2,b=3 ( a + b ) 2 = 2 a b (a+b)^{2}=2ab − 2 ( a 2 + b 2 ) = a b -2(a^{2}+b^{2})=ab

Margaret Zheng by Margaret Zheng , 20, USA

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1 solution

Genis Dude
Aug 22, 2016

If,2a²+2b²+ab/a^3+b^3=0 Then 2a²+2b²+ab must be 0 If,2a²+2b²+ab =0 Then 2a²+2b²=-ab (subtracting ab on both sides) →2(a²+b²)=-ab Therefore, -2(a²+b²)=ab

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