Question

The difference of squares of two number is 180 the square of the smaller number is 8 times the larger number find the number

Answer 1

Answer:

smaller number be y

and larger be x

x^2 - y^2 = 180 ----- (a)

given y^2 = 8 x -------(1)

put eq (1) in eq (a)

x^2 - 8x = 180

x^2 -8x - 180 = 0

x^2 - 18x + 10x -180 =0

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

x-18 =0 , x+10=0

x= 18 , x=-10

now eq (1)

y^2=8x

y^2= 8*18= 144

y=√144

y=+12 , -12

Ans : x = 18

y= 12