Question

The difference of square of two number is 180.The square of the smaller number is 8 time the larger number.find the two number​

Answer 1

Answer:

The required numbers are 18 & 12.

Step-by-step-explanation:

Let the greater number be x.

And the smaller number be y.

From the first condition,

x² - y² = 180 - - ( 1 )

From the second condition,

y² = 8x - - ( 2 )

Now,

x² - y² = 180 - - ( 1 )

⇒ x² - 8x = 180

⇒ x² - 8x - 180 = 0

⇒ 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

Now, by substituting x = 18 in equation ( 2 ), we get,

y² = 8x - - ( 2 )

⇒ y² = 8 * 18

⇒ y² = 144

⇒ y = ± 12

∴ y = 12

∴ The required numbers are 18 & 12.

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Verification:

The square of greater no. - The square of smaller no. is equal to 180.

⇒ x² - y² = 180

⇒ ( 18 )² - ( 12 )² = 180

⇒ 324 - 144 = 180

⇒ 180 = 180

Hence verified!

Answer 2

Step-by-step explanation:

Assume that the one number is x and other number is y.

The difference of square of two number is 180.

As per given condition,

→ x² - y² = 180 .............................(1)

Also said that the smaller number is 8 time the larger number.

Assume that y is the smaller one and x is the larger one.

So,

→ y² = 8x

Substitute value of x in (1)

→ x² - 8y = 180

→ x² - 8y - 180 = 0

Split the middle term

→ x² - 18x + 10x - 180 = 0

→ x(x - 18) + 10(x - 18) = 0

→ (x + 10)(x - 18) = 0

→ x = 18 (Negative one neglected)

Now,

→ y² = 8(18)

→ y² = 144

→ y = 12

Hence, the two numbers are 18 and 12.