Problem: The roots of x2−415−x−22=1 are
Answer Choices:
A. -5 and 3
B. ±2
C. only 2
D. -3 and 5
E. only 3
Solution:
Multiply both sides of the equation by x2−4=(x+2)(x−2).
15−2(x+2)=x2−4;∴x2+2x−15=0;
and ∴x=−5 or x=3. Each of these roots satisfies the original equation.