Question

The difference of squares of two numbers is 180. the square of smaller no. is 8 times the larger number. find the two numbers .

Answer 1

Let the larger no. be x and the smaller one be y.
 Then, x(square)-y(square) = 180 ...(given)
and 8x=y(square)... (given)

Solving both, we get

x(square) - 8x - 180 = 0
then solving this, we get
x = 18 or -10

So, case 1 : 
When x = 18 
Then smaller no. is 8x = y(square)
  i.e 8(18) = y (square)
 ⇒ y = +/- 12

Case 2 :
When x = -10
Then smaller no. is 8x = y(square)
i.e 8(-10) = y(square)
⇒ x = under root -80

This is not possible

Therefore x = 18 and y = +/-12

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the 1st required number be x.

And the 2nd number be y.

Such that x > y.

Then, x² - y² = 180 ..... (i)

And, y² = 8x ....(ii)

According to the Question,

From (i) and (ii), we get

⇒ 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, - 10 (As x can't be negative)

⇒ x = 18

Putting x's value in Eq (ii), we get

⇒ y² = 8x

⇒ y² = 8 × 18

⇒ y² = 144

⇒ y = ± 12

Hence, the numbers are 18 and 12 or 18 and - 12.