2a+b=11 and 4a^2 +b^2=101, what is the value of ab?
A 4
B5
C12
D6
E20
b = 11 - 2 a
4 a^2 +11-2a = 101
4 a^2 - 2 a - 90 = 0
2 a^2 - a - 45 = 0
a = 5 or -9/2
if a = 5, 10+b = 11 so b = 1 and ab=5
check:
4(25) +1 = 101??? yes :)
if a = -9/2 , -9 + b = 11 and b = 20
check
4(49/4) + 400 = 101 NO WAY
so use first root and
ab = 5