Question

Cornell solved the radical equation x2+3x+2−−−−−−−−−√=x2−3−−−−−√−1
and found x=−2
. What is the other solution of this radical equation? Enter your answer as a fraction or select no other solution if x=−2
is the only solution.(1 point)

x = -165

x = -145

x = -192


no other solution

Answer 1

The other solution is x = -14/5.

Work: sqrt(x^2+3x+2) = sqrt(x^2-3) - 1. Let A = sqrt(x^2+3x+2) ≥ 0. Then sqrt(x^2-3) = A+1. Squaring and simplifying gives A = -(3/2)(x+2). Squaring again yields 5x^2 + 24x + 28 = 0, with roots x = -2 and x = -14/5. Both satisfy the original equation, so the other solution is -14/5 (option shown as -145).