solve for x

1>a>3/4

x^3(x+1)=(x+a)(2x+a)

without using a calculator/ wolphram!

Do you want help on it or just as a challenge?

Do you want help on it or just as a challenge?

challenge

x^4+x^3-2x^2-3ax-a^2=0

x^3+x^2-2x=\dfrac{a^2}{x}+3a

x(x+2)(x-1)=\dfrac{a^2}{x}+3a

sketch LHS

sketch RHS

find points of intersection

thats not an exact solution. u cheater! All you can find doing this is the number of solutions and a range of values each solution takes.

(edited 13 years ago)

Unparseable latex formula:

\\ x^3(x+1) = (x+a)(2x+a) \\[br]\implies (x^2 - x - a)(x^2 + 2x + a) = 0

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