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 the two numbers.
Answer» Let the larger number = x Then the square of the smaller number = 8 times the larger number = 8x and the square of the larger number = x² According to the question, x² - 8x = 180 => x² - 8x - 180 = 0 => x² - 18x + 10x - 180 = 0 => x(x - 18) + 10(x - 18) = 0 => (x - 18) (x + 10) = 0 => x - 18 = 0 or x + 10 = 0 => x = 18 or x = -10 Thus, the larger number = 18 or -10 Then, the square of the smaller number = 8(18) or 8(-10) = 144 or -80 The square of a number can't be negative, so, the square of smaller number = 144 Hence, the smaller number = sqrt(144) = 12 The numbers are 12 and 18

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

Answer»

Let the larger number = x

Then the square of the smaller number = 8 times the larger number = 8x

and the square of the larger number = x²

According to the question,

x² - 8x = 180

=> x² - 8x - 180 = 0

=> x² - 18x + 10x - 180 = 0

=> x(x - 18) + 10(x - 18) = 0

=> (x - 18) (x + 10) = 0

=> x - 18 = 0 or x + 10 = 0

=> x = 18 or x = -10

Thus, the larger number = 18 or -10

Then, the square of the smaller number = 8(18) or 8(-10)

= 144 or -80

The square of a number can't be negative, so, the square of smaller number = 144

Hence, the smaller number = sqrt(144) = 12

The numbers are 12 and 18