Question

The difference of squares of two numbers is 180 the square of smaller number is 8 times the larger number. Find the two number

100% of making brainleist​

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

Answer 2

Answer:

$x = 18 \: or \: x = - 10 \: {rejected}$

Step-by-step explanation:

Let the two numbers be ,

$x {}^{2} \: and \: y {}^{2}$

According to the given first condition,

$x {}^{2} - y {}^{2} = 180$

According to the given second condition,

$y {}^{2} = 8x$

Therefore, by substituting the value of

$y {}^{2} \: into \: the \: equation \: x {}^{2} - y {}^{2} = 180$

$x {}^{2} - y {}^{2} = 180 \\ x {}^{2} -8x = 180 \\ x {}^{2} - 8x - 180 = 0 \\ x{}^{2} - 18x + 10x - 180 = 0 \\ x(x - 18) + 10( x- 18) = 0 \\ (x - 18)(x + 10) = 0 \\ therefore \: x = 18 \: or \: x = ( - 10)$

So, we got x=18 and x= -10 (rejected)

For y , we have to substitute the value of x=18 into the equation y^2=8x .

$y {}^{2} = 8x \\ y {}^{2} = 8 \times (18) \\ y {}^{2} = 144 \\ y = + - 12$

We got the two numbers desired in the question.

FOLLOW ME AND MARK MY ANSWER AS BRAINLIEST