Question

Help please, I'm clueless...
(2(x^2 + x + 1)^1/4 = (16x^2 + 10x - 14)^1/4

Answer 1

On the left hand side you opened 2 parenthesis but only closed one. I'm assuming this is what you meant. And you are solving for x?
\[2(x^2+x+1)^\frac{ 1 }{ 4 } = (16x^2+10x-14)^\frac{ 1 }{ 4 }\]
If you raise both sides to the 4th power you get:
\[16(x^2+x+1)=16x^2+10x-14\]
Distribute the 16 on the left side.
\[16x^2+16x+1 = 16x^2+10x-14\]
If you subtract everything from the right hand side you get.
\[6x+30=0\]
Factor \[6(x+5)=0\]
Divide by 6
\[x=5\]

Answer 2

Thank you!