Question

The average of a non-zero number and its square is 11 times the number. The number is ?

Answer 1

We have,
(x and x²)'s average = 11x

So,
x+x²/2=11x
x+x²=22x
x²=22x-x
x²=21x
x²-21x=0
x(x-21)=0. (Taking common)

Therefore, we can say that either x is 0 or (x-21) is 0.