Paul is x years old and his father's age is twice the square of Paul's

1.	Paul is x years old and his father's age is twice the square of Paul's age . Ten years hence , father's age will be 4 times Paul's age. find their present ages .
Answer» Let, Pauls's present age be x. So his father's age will be 2(x²) A/Q, 2x² +10 = 4(x+10) 2x² + 10 = 4x + 40 2x² - 4x = 40-10 2x² -4x = 30 2x² -4x - 30 = 0 2x² - 10x + 6x - 30 = 0 2x(x-5) + 6(x-5) = 0 (2x + 6) (x-5) = 0 2x + 6 = 0 or x - 5 = 0 2x = -6 or x = 5 x = -6/2 or x = 5 x = -3 or x = 5 So x = -3, 5 So the age should be in negative value therefore present age of paul is 5 years and his father's age 2(5)² = 2 x 25 = 50 years.

Paul is x years old and his father's age is twice the square of Paul's age . Ten years hence , father's age will be 4 times Paul's age. find their present ages .

Answer»

Let,

Pauls's present age be x.

So his father's age will be 2(x²)

A/Q,

2x² +10 = 4(x+10)

2x² + 10 = 4x + 40

2x² - 4x = 40-10

2x² -4x = 30

2x² -4x - 30 = 0

2x² - 10x + 6x - 30 = 0

2x(x-5) + 6(x-5) = 0

(2x + 6) (x-5) = 0

2x + 6 = 0 or x - 5 = 0

2x = -6 or x = 5

x = -6/2 or x = 5

x = -3 or x = 5

So x = -3, 5

So the age should be in negative value therefore present age of paul is 5 years and his father's age 2(5)² = 2 x 25 = 50 years.