Problem: The symbol ≥ means "greater than or equal to"; the symbol ≤ means "less than or equal to". In the equation (x−m)2−(x−n)2=(m−n)2,m is a fixed positive number, and n is a fixed negative number. The set of values x satisfying the equation is:
Answer Choices:
A. x≥0
B. x≤n
C. x=0
D. the set of all real numbers
E. none of these
Solution:
(x−m)2−(x−n)2=(m−n)2m>0n<0
Since (m−n)2>0(x−m)2>(x−n)2
∴ ∣x−m∣>∣x−n∣
x−m>x−n
not usable
2x<m+n
x<2m+n
or
Solving for x we have x(−m+n)=−mn+n2 x=n