Question

find two natural numbers which differ by 5 and whose square have the sum 125 solve the quadratic equation word problem​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• The two numbers are 5 and 10.

☆ɢɪᴠᴇɴ☆

• Two natual number differ by 5.
• Sum of their squares is 125

✫ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ✫

Let $n$ and $n+5$ be the two natural numbers, then

$\to n^2 + (n + 5)^2 = 125$

$\to n^2 + n^2 + 10n + 25 = 125$

$\to 2n^2 + 10n - 100 = 0$

$\to 2n^2 - 10n + 20n - 100 = 0$

$\to 2n(n - 5) + 20(n - 5) = 0$

$\to (n - 5)(2n + 20) = 0$

$\to n = 5\:or\: - 10$

Since n is a natural number, n cannot be negative.

$\to n = 5$

Thus one of the number is 5.

The other number is given by

$\to n + 5$

$\to 5 + 5$

$\to 10$