Question

the difference of squares of 2 numbers is 180 the squares of the smaller number is 8 times the larger number find the 2 numbers

Answer 1

Let the larger number = x & smaller number = y
then acc to given condition, x^2 - y^2 = 180 (1)
& y^2 = 8x (2)
Put (2) in (1), we have
x^2 - 8x = 180
⇒ x^2 - 8x -180 = 0
⇒ x^2 - 10x+18x -180 = 0
⇒x(x+10) -18(x+10) = 0
⇒(x-18) (x+10) = 0
⇒ x= 18 or x= -10 (x cannot be -ve, so x=18)
If x= 18 then y = √8*18 = √144 = +12,-12 ( using equation 2)

Answer 2

A²-B²=180
B²=8A
A²-8A-180=0
A²-10A+18A-180=0
A[A-10]+18[A+10]=0
[A+18][A-10]=0
either A=-10 OR 18 [BUT IT CANT BE NEGATIVE AS IT IS SQUARE NUMBER]
SO A=18
B=√8×18
B=12