Question

the age of father is twice the square of the age of his son.eight years later the age of the father will be4 years more than three times age of his son.find the present age of father and son????
step wise answer plzzz

Answer 1

let the age of son = x
father's age is twice the square of his son's age
so age of father = 2x²

after 8 years,
age of son = x+8
age of father = 2x²+8
given that father will be 4 years more than 3 times age of son
so 2x²+8 = 3(x+8) + 4
⇒2x² + 8 = 3x + 24 + 4
⇒2x² + 8 = 3x + 28
⇒ 2x² + 8 - 3x - 28 = 0
⇒2x² - 3x - 20 = 0
⇒2x² - 8x + 5x - 20 = 0
⇒2x(x-4) + 5(x-4) = 0
⇒(2x+5)(x-4)=0
⇒x = 4 or x = -5/2

age can't be negative.
So age of son is 4 years.
age of father = 2x² = 2×4² = 32 years