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.............(it's a sum of Quadratic Equations!!!!)

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 the larger number be x.

Square of larger number = x²

Then the square of smaller number = 8 times the larger number = 8x

ATQ,

x² - 8x = 180

x² - 8x - 180 = 0

By factorisation,

x² - 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

Taking x = 18 we get,

Larger number = x = 18

ѕmαllєr numвєr = √(8x) = √(8×18) =√144 = 12

Taking x = -10

Larger number = -10

Smaller number. = √(8x) = √(8×-10) = √-80
Not possible .


Hence the two numbers are 18 and 12.

:)