Question

the sum of two number is five, the difference of the their square is 5 find the difference of the number​

Answer 1

QUESTION:

The sum of two numbers is 5 and the difference of their squares is 5. How would one find the difference between the numbers?

ANSWER:

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

So the difference between the two numbers is 1