Given x^(1/2)-5x^(1/4)+6=0 , find x. I tried but couldn't get the correct answer. The answers given are 16 and 81. Please kindly show the working as well. Thanks.
$\displaystyle \displaystyle x^{1/2} - 5x^{1/4} + 6 = 0$
$\displaystyle \displaystyle (x^{1/4})^2 - 5x^{1/4} + 6 = 0$.
Let $\displaystyle \displaystyle X = x^{1/4}$ and the equation becomes
$\displaystyle \displaystyle X^2 - 5X + 6 = 0$
$\displaystyle \displaystyle (X - 2)(X - 3) = 0$
$\displaystyle \displaystyle X - 2 = 0$ or $\displaystyle \displaystyle X - 3 = 0$
$\displaystyle \displaystyle X = 2$ or $\displaystyle \displaystyle X = 3$
$\displaystyle \displaystyle x^{1/4} = 2$ or $\displaystyle \displaystyle x^{1/4} = 3$
$\displaystyle \displaystyle x = 2^4$ or $\displaystyle \displaystyle x = 3^4$
$\displaystyle \displaystyle x = 16$ or $\displaystyle \displaystyle x = 81$.