Question

The difference of squares of two numbers is 180 the square of the smaller number is 8 times the large no.find the two noumber

Answer 1

let large number is x

so it's square is x^2

let small number is y

so it's square is y^2

now according to given condition ,

x-2 - y^2 = 180

but , y^2 = 8x


so , x-2 - 8x - 180 = 0

x-2 - 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

but x = - 10 is not possible

so x = 18

I.e. larger number is 18


so smaller is , y^2 = 8 × 18

y^2 = 144

y = 12