Cambridge University Entrance Interview | Find x=?

[@RyanLewis-Johnson-wq6xs]

Sqrt[3x+Sqrt[4x]]=x x=0 x=4

[@НеллиПшено]

Решаем графически систему уравнений. y=x y=(3х+√4x) ^1/2 x=0 x=4 Good luck!

[@kareolaussen819]

Note that the rule a^m * b^m = (a * b)^m does not always hold when m is not an integer: Take a=b=-4, and m=1/2. Then left hand side equals √-4 * √-4 = 2i * 2i =-4, the right hand side √(-4 * -4)=√16=4.

[@hevado01]

First factor out sqrt(x) to get x=0 and be left with a quadratic in sqrt(x) for the other one

[@kareolaussen819]

This is not quite correct, one still has to solve a cubic equation.

[@hevado01]

@@kareolaussen819you’re right, you can only factor out x^1/4 which leaves a cubic

[@cabasantbab]

X=4