A man is 5 times as old as his son. 2 years ago the sum of the squares of their ages was 1114. Find the present age of son.
- 7 years
- 9 years
- 8 years
- 8 1/2 years
- 6 years
Let son's age = x, then
father's age = 5x
As before 2 years ago the sum of the squares of their ages was 1114, the equation becomes as
\((x - 2)^2 + (5x - 2)^2 = 1114 \)
By simplifying the equation, we have
\(13x^2 -12x -553 = 0\)
Now solving the equation, we have
\(13x^2 - 12x - 553 = 0\)
\(13x^2 - 91x + 79x -553 = 0\)
13x(x - 7) + 79(x - 7) = 0
(x - 7)(13x + 79) = 0
x = 7 and x = -6.077
As age could not be negative, hence the present age of the son is 7 years.