Question

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 1

Hi !

Larger no: = x 

Smaller no: = y

According to the question,

8x = y²              -----> (1)

Also,
x² - y² = 180

from (1),

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 , x = -10

Only the positive value of "x" is taken .

x = 18

8x = y²

8*18 = y²

144 = y² , y = √144

y = 12

Hence, the no:s are 12 and 18 

Answer 2

Heya,

Assume that,

Larger number = a
Smaller number = b

ATQ,

It given that,
》The difference of squares of two numbers is 180.

a^2 - b^2 = 180

》The square of the smaller number is 8 times the larger number.

8a = b

a^2 - 8a = 180

a^2 - 8a - 180 = 0 [Splitting the middle term]

a^2 - 18a - 10a - 180 = 0

a (a - 18) + 10 (a - 18) = 0

(a - 18) (a - 10) = 0

a = +18 & a = -10

Positive value of "a" is taken.

a = 18

8a = b^2

8 × 18 = b^2

144 = b^2

√144 = b

√12 × 12 = b

12 = b

Therefore,

The numbers are 18 & 12.

Hope my answer helps you :)

Regards,
Shobana