Solve the following equation: √(4 - 3√(10 - 3x)) = x - 2.
Solution
Answer: x = 3.
Squaring twice we get x4 - 8x3 + 16x2 + 9x - 90 = 0. Factorising, we get (x + 2)(x - 3)(x2 - 7x + 15), so the only real roots are x = -2 and 3. Checking, we find that 3 is indeed a solution of the original equation, but x = -2 is not because we get √(-8) on the lhs.
Thanks to Suat Namli for a similar solution.
© John Scholes
jscholes@kalva.demon.co.uk
21 Nov 2002
Last updated/corrected 21 Nov 02