How do you solve #x-3 = sqrt(x+27)#?
1 Answer
Square both sides to get a quadratic to solve, then find which solution of the quadratic is a solution of the original equation.
Explanation:
Start by squaring both sides, but note that this typically introduces spurious solutions. That is, the resulting equation may have solutions that the original does not.
#x+27 = (x-3)^2=x^2-6x+9#
Subtract
#0 = x^2-7x-18 = (x-9)(x+2)#
(I found this factorisation by finding a pair of factors
This has solutions
The value
#x-3 = -2-3 = -5 != 5 = sqrt(-2+27) = sqrt(x+27)#
The value
#x-3 = 9-3 = 6 = sqrt(36) = sqrt(9+27) = sqrt(x+27)#