Question

There are two ways of adding two square numbers to make 65. Write a different square number in each box. [ ] + [ ].

Answer 1

I found those two possibilities, hopefully they're correct:

8² + 1² = 8 * 8 + 1 * 1 = 64 + 1 = 65
7² + 4² = 7 * 7 + 4 * 4 = 49 + 16 = 65

I hope it will help you :)

Answer 2

The answers are:

`1^2+8^2=65\\4^2+7^2=65`

Explanation:

In order to determine the pairs of numbers, we have to know about the equation of this case.

Given:

x=first number

y=second number

`x^2+y^2=65`

With this equation, we can find a lot of pairs of numbers which fulfill the equation. But, in case that we need just whole numbers, we only have to replace a whole number in any variable and determine the value of the other variable.

`x=1\\1^2+y^2=65\\y^2=65-1\\y^2=64\\y=√(64)\\y=8\\1^2+8^2=65`

`x=4\\4^2+y^2=65\\y^2=65-16\\y^2=49\\y=√(49)\\y=7\\4^2+7^2=65`

Finally, the two pairs of numbers are:

`1^2+8^2=65\\4^2+7^2=65`