Question

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

Answer 1

Answer:

smalwr number is 12 and larger is 18

Answer 2

Answer:

The smaller number is 12 and the larger one is 18.

Step-by-step explanation:

Here we have been given that the difference of the squares of the 2 numbers is given to be 180. Also, we have that the square of the smaller among the two is 8 times the larger one.

Therefore we have the following:

Let the larger number be n.

It has been given that the smaller number square if 8 times the larger one.

Square of smaller number = 8n

Now we have,

$n^{2} - 8n = 180$

⇒$n^{2} - 8n - 180 = 0$

⇒ $n^{2} - (18 - 10)n - 180 = 0$

⇒$n^{2} - 18n + 10n - 180 =0$

⇒ $n(n-18) + 10(n-18) = 0$

⇒ (n + 10) (n-18) = 0

∴ n = -10 or 18

The larger number is therefore 18.

∴ Smaller number = $\sqrt{8n}$

= $\sqrt{8(18)}$

= $\sqrt{144}$

= 12

Therefore the smaller number is 12.