Question

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

Answer 1

Answer:

Let the numbers be ‘a’ and ‘b’.

Given, difference of the squares of two numbers is 180.

 

⇒ a2 – b2 = 180

 

Also, square of the smaller number is 8 times the larger.

⇒ b2 = 8a

Thus, a2 – 8a – 180 = 0

⇒ a2 – 18a + 10a – 180 = 0

⇒ a(a – 18) + 10(a – 18) = 0

⇒ (a + 10)(a – 18) = 0

 

⇒ a = -10, 18

Thus, the other number is

 

324 – 180 = b2

 

⇒ b = �12

 

Numbers are 12, 18 or -12, 18

Answer 2

Step-by-step explanation:

Let the no be x

So its square would be x²

It larger one will be 8x²

8x²-x²=180

7x²=180/7

x²= 25 (approximately )

x=5

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