Find-x-if-3-x-x-12-

Question Number 85198 by otchereabdullai@gmail.com last updated on 19/Mar/20

Find x if^{3} \sqrt{x} + \sqrt{x} = \sqrt{12}

Answered by MJS last updated on 19/Mar/20

let x = y^{6}

y^{3} + y^{2} - \sqrt{12} = 0

let y = z - \frac{1}{3}

z^{3} - \frac{1}{3} z + \frac{2}{27} - 2 \sqrt{3} = 0

D = 4 {(- \frac{1}{3})}^{3} + 27 {(\frac{2}{27} - 2 \sqrt{3})}^{2} > 0 \Rightarrow

\Rightarrow if you need an exact solution use

{Cardano}^{'} s formula

z \approx 1.57613

y \approx 1.24280

x \approx 3.68470

is the only solution \in C

Commented by otchereabdullai@gmail.com last updated on 19/Mar/20

Thanks a lot prof MJS you are funtastic

God bless you