Question

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

Answer 1

Answer:

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

Step-by-step explanation:

( Or)

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.

:)