## Online Course Discussion Forum

### MC III Algebra help

MC III Algebra help

3.31:

My equations are:

$$a^4-4a \geq0$$

$$x= (-a^2+ \sqrt{a^4-4a})/2$$

But I don't know how to get the maximum value, I tried completing the square but it didn't work.

3.34:

I started with $$20x=x^2+y^2$$,

then I got $$x^3-y^3-18xy = (x+y)(x^2-xy+y^2)-18y=(x+y)(20x-xy)-18xy=x((x+y)(20-y)-18y)$$

I got x=0 or y = 0, and (x+y)(20-y)-18xy=0. however, I can't figure out how to solve the equation.

3.35:

I substituted $$a= \sqrt[5]{x-6}$$ and $$b=\sqrt[5]{39-x}$$,

and I got ab(a+b)(a^2+b^2)=30. I tried c = ab and d=a+b, but It didn't really work out.