Question
(Sqrtx^2+5x-2)-(sqrtx^2+5x-5)=1
Answers
oobleck
√(x^2+5x-2) - √(x^2+5x-5) = 1
square both sides to get
x^2+5x-2 - 2√((x^2+5x-2)(x^2+5x-5)) + x^2+5x-5 = 1
2x^2 + 10x - 8 = 2√((x^2+5x-2)(x^2+5x-5))
(x^2+5x-4)^2 = (x^2+5x-2)(x^2+5x-5)
x^2 + 5x - 6 = 0
x = -6,1
square both sides to get
x^2+5x-2 - 2√((x^2+5x-2)(x^2+5x-5)) + x^2+5x-5 = 1
2x^2 + 10x - 8 = 2√((x^2+5x-2)(x^2+5x-5))
(x^2+5x-4)^2 = (x^2+5x-2)(x^2+5x-5)
x^2 + 5x - 6 = 0
x = -6,1