Find Coeff. of x^{88} & Solve for x

[mercedesbenz]

[SOLVED] please hint me

Homework Statement

28. What is the coefficient of $$x^{88}$$ from
$$(x+1)(x+2)(x-3)(x+4)(x+5)(x-6)...(x+88)(x+89)(x-90)$$.

29. Find x from this equation $$\frac{108}{\sqrt{x^2-2916}}=\frac{378-x-\sqrt{x^2-2916}}{x+54}$$.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

28. What is the coefficient of $$x^{88}$$ from
$$(x+1)(x+2)(x-3)(x+4)(x+5)(x-6)...(x+88)(x+89)(x-90)$$.

Hi mercedesbenz!

ok … a hint, as you asked for …

First, try answering: what are the coefficients of $$x^{90}$$ and of $$x^{89}$$ ?

29. Find x from this equation $$\frac{108}{\sqrt{x^2-2916}}=\frac{378-x-\sqrt{x^2-2916}}{x+54}$$.

You can simplify this slightly, before solving it:

Hint: what is √2916? What is 378/√2916?

 

[mercedesbenz]

Thank you so much I've already solved it.