how do you solve(x+5)^1/2-(5-2x)^1/4

Question

I don't uderstand how to solve this because it has 1/2 as one exponent and the other one is 1/4.

Answer 1

This is not an equation because there's no equals sign.

So do you mean: (x+5)^½=(5-2x)^¼?

If so:

Square both sides:

x+5=(5-2x)^½, then square again:

x²+10x+25=5-2x,

x²+12x+20=0=(x+2)(x+10) so x=-2 or -10, but we must test these apparent solutions:

x+5=3 or -5; 5-2x=9 or 25. But if x+5=-5 we get (-5)^½=√-5 which is not real (it's complex). So the only real solution is x=-2.