Question

The sum of the two number is 5 and difference of their squares is 5. Find the difference of the numbers?​

Answer 1

Step-by-step explanation:

Let m and n be the two numbers.

Then m+n = 5.

And n²-m² = 5.

So m = 5-n.

So n² - (5-n)² = 5.

So n² - (5²–2×5n+n²) = 5.

So n² - (25–10n+n²) = 5.

So n²–25+10n-n² = 5.

So 10n-25 = 5.

So 10n = 5+25 = 30.

So n = 30/10 = 3.

And m - 5-n = 5–3 = 2.

So the two numbers are 2 and 3.

CHECK:

2+3 = 5. [CORRECT]

3²–2² = 9–4 = 5. [CORRECT]

Therefore the difference between the two numbers is 3–2 = 1 or 2–3 = -1.

So the difference between the two numbers is 1 or -1.

Answer 2

Step-by-step explanation:

Let the number be X and Y

Given that sum of two numbers is 5.

= X+Y = 5 -------- 1

Given that Difference of their square is 5.

= X '2 - Y ' 2 = 5

we know that a'2 - b'2 = ( a+b ) ( a-b)

= ( X + Y) ( X - Y) = 5

= ( 5) ( X - Y) = 5

= ( X - Y) = 1