Question

the differences of two numbers is 180.the square of smaller number is 8 times the larger number.Find the number

Answer 1

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

→Numbers are 12, 18 or -12, 18

Answer 2

let the larger no. be x.
therefore, smaller no. be 8x.
hence, (x)2 - (8x)2 = 180
x - 64x = 180
x (64 - 4)= 180
60x = 180
x = 180/60
x = 3