Problem:
If y+4=(xβ2)2, x+4=(yβ2)2, and xξ =y, what is the value of x2+y2?
Answer Choices:
A. 10
B. 15
C. 20
D. 25
E. 30
Solution:
Expanding the binomials and subtracting the equations yields x2βy2=3(xβy). Because xβyξ =0, it follows that x+y=3. Adding the equations gives x2+y2=5(x+y)=5β 3=(B)15β.
Note: The two solutions are (x,y)=(23β+221ββ,23ββ221ββ) and (23ββ221ββ,23β+221ββ).