Problem: The equality (x+m)2β(x+n)2=(mβn)2, where m and n are unequal nonzero constants, is satisfied by x=am+bn where:
Answer Choices:
A. a=0, bβ has a unique non-zero value
B. a=0,bβ has two non-zero values
C. b=0, aβ has a unique non-zero value
D. b=0, aβ has two non-zero values
E. aβ and bβ each have a unique non-zero value.
Solution:
(x+m)2β(x+n)2=(mβn)2
Factor the left side of the equation as the difference of two squares.
(x+mβxβn)(x+m+x+n)=(mβn)2
(mβn)(2x+m+n)=(mβn)2
Since mξ =n;2x+m+n=mβn,x=βn, so that (A) is the correct choice.