The difference of squares of two numbers is 180. The square of the sma

1.	The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Answer» Let the numbers be ‘a’ and ‘b’. Given, difference of the squares of two numbers is 180. ⇒ a² – b² = 180 Also, square of the smaller number is 8 times the larger. ⇒ b²= 8a Thus, a² – 8a – 180 = 0 ⇒ a² – 18a + 10a – 180 = 0 ⇒ a(a – 18) + 10(a – 18) = 0 ⇒ (a + 10)(a – 18) = 0 ⇒ a = -10, 18 Thus, the other number is 324 – 180 = b² ⇒ b = 12 Numbers are 12, 18 or -12, 18

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

Answer»

Let the numbers be ‘a’ and ‘b’.

Given, difference of the squares of two numbers is 180.

⇒ a² – b² = 180

Also, square of the smaller number is 8 times the larger.

⇒ b²= 8a

Thus, a² – 8a – 180 = 0

⇒ a² – 18a + 10a – 180 = 0

⇒ a(a – 18) + 10(a – 18) = 0

⇒ (a + 10)(a – 18) = 0

⇒ a = -10, 18

Thus, the other number is 324 – 180 = b²

⇒ b = 12

Numbers are 12, 18 or -12, 18