Question

The difference of Suqare of two numbers is
180. The square of smaller number is 8
time the large number.Find two number.​

Answer 1

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

★ The difference of Suqare of two numbers is 180. The square of smaller number is 8 time the large number.Find two number.

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✒ The numbers are 12 and 18.

$\mathtt{\huge{\underline{\orange{Solution:-}}}}$

Given :-

• The difference of Suqare of two numbers is 180.

• The square of smaller number is 8 time the large number.

To Find :-

• The two number.

Calculation :-

Let the larger number be x.

According to the question,

• The square of smaller number is 8 time the large number.

=> 8 × x

=> 8x

The difference of Suqare of two numbers is 180.

➝ 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 | x + 10 = 0

➝x = 18 | x = -10

So our larger number is 18 . { We can't take square root of a negative number. }

We have smaller number 8x = 8 × 18 = 144

Now, square of smaller number = 144.

Hence, the smaller number = √144 = 12

So , 12 and 18 are numbers.

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Answer 2

Given:

The difference between the square of two numbers is 180

The square of the smaller number is 8.

To find:

The two numbers

So,

Let the large number be x

So, the square of the smaller number is 8  time the large number

Let the square smaller number be (8 * x ) = 8x

Now,

According to the question:

⇒ x² - (8x) = 180

⇒ x² - 8x - 180 = 0

⇒ x² - 18x + 10x - 180

[By middle term spliting]

⇒x(x - 18) + 10(x - 18)

⇒ (x + 10)(x - 18)

So,

x = -10

And

x = 18

Thus,

The large number be (-10) and 18

- - -

Check

• CASE 1

x = -10

The large number is x = (-10),

The square of large number = (-10)*(-10) = 100

The square of smaller number is 8x = 8*(-10) = -80

Now,

The difference between the square of two number

= 100 - (-80)

= 100 + 80

= 180

Also,

• CASE 2

x = 18

The large number is x = 18,

The square of large number = (18)*(18) = 324

The square of smaller number is 8x = 8*(18) = 144

Now,

The difference between the square of two number

= 324 - 144

= 180

Now,

The numbers are

From case 2

The large number is 18

And the small number is $\sqrt{144}$ = 12

[Note: we can't find √-80 so, we can't take numbers of case one when numbers are asked in square roots.]

$\boxed{\red{Numbers\ are =18, 12}}$