GMAT Problem Solving (PS) | Re: New Algebra Set!!!

SOLUTIONs:

1. If \(x=\sqrt[4]{x^3+6x^2}\), then the sum of all possible solutions for x is:

A. -2
B. 0
C. 1
D. 3
E. 5

Take the given expression to the 4th power:\(x^4=x^3+6x^2\) ;

Re-arrange and factor out x^2:\(x^2(x^2-x-6)=0\) ;

Factorize: \(x^2(x-3)(x+2)=0\) ;

So, the roots are\(x=0\) ,\(x=3\) and\(x=-2\) . But\(x\) cannot be negative as it equals to the even (4th) root of some expression(\(\sqrt{expression}\geq{0}\) ), thus only two solution are valid\(x=0\) and\(x=3\) .

The sum of all possible solutions for