One year ago, a father was 8 times as old as his son. Now, his age is the square of his son’s age. Find the age of the father

Let's denote the current age of the son as x (in years).

According to the problem, one year ago, the son was x - 1 years old and the father was 8 times as old as his son. So, the father was 8 * (x - 1) = 8x - 8 years old.

Now, the father's age is the square of his son's age. So, the father is now x^2 years old.

But we also know that the father is one year older than he was last year. So, we can set up the equation:

8x - 8 + 1 = x^2

Solving this equation will give us the current age of the son, and squaring that result will give us the current age of the father.

Let's solve it:

8x - 7 = x^2

Rearranging terms gives us:

x^2 - 8x + 7 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here, a = 1, b = -8, and c = 7.

Substituting these values into the quadratic formula gives us:

x = [8 ± sqrt((-8)^2 - 417)] / (2*1) x = [8 ± sqrt(64 - 28)] / 2 x = [8 ± sqrt(36)] / 2 x = [8 ± 6] / 2

So, the possible solutions are x = 7 or x = 1.

Since age cannot be negative, we discard x = 1 as it would imply the son was 0 years old one year ago, which is not possible given the father was 8 times as old as his son at that time.

Therefore, the son is currently 7 years old and the father, being the square of the son's age, is 49 years old.