Question

Arun's age after six years will be the square of his age six years ago. current age?​

Answer 1

Answer:

Arjun's current age is 10 years.

Step-by-step-explaination:

Let Arjun's current age be x years.

Arjujn's age six years after = ( x + 6 ) years.

Arjun's age six years before = ( x - 6 ) years.

From given condition

Arjun's age after six years = Square of Arjun's age before six years

∴ ( x + 6 ) = ( x - 6 )²

⇒ ( x + 6 ) = x² - 12 x + 36

⇒ x + 6 = x² - 12 x + 36

⇒ x² - 12 x + 36 - x - 6 = 0

⇒ x² - 13 x + 30 = 0

⇒ x² - 10 x - 3 x + 30 = 0

⇒ x ( x - 10 ) - 3 ( x - 10 ) = 0

⇒ ( x - 10 ) ( x - 3 ) = 0

⇒ x - 10 = 0 or x - 3 = 0

⇒ $\boxed{\red{\sf\:x = 10}}$ or $\boxed{\red{\sf\:x = 3}}$

But, x = 3 is not considerable.

Hence, x = 10 years.

Arjun's current age is 10 years.