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

Let the larger number = x
Then the square of the smaller number = 8 times the larger number = 8x
and the square of the larger numbe r = x
According to the question,
x - 8x = 180
=> x - 8x - 180 = 0
=> x - 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
Thus, the larger number = 18 or -10
Then, the square of the smaller number = 8(18) or 8(-10)
= 144 or -80
The square of a number can't be negative, so, the square of smaller number = 144
Hence, the smaller number = sqrt(144) = 12
The numbers are 12 and 18
hope it helps u
mark it as brainliest answer pls

Answer 2

let x be the bigger number
and y be the smaller number

given, x^2 - y^2 = 180 & y^2= 8x

so, substituting value of y^2 in first equation we get ,

x^2 -8x -180 =0
x^2 -18x + 10x -180 = 0
x(x-18) +10(x-18)=0

therefore, x= 18