Question

Help please !!!!!!!!!!!!!!!!!!

Answer 1

n = 59

Explanation:

There's definitely a better way, i just did math randomly but here goes:

First i squared both sides. which gets you:

`(√(n+5)-√(n-10) )(√(n+5)-√(n-10) )=1^2\\\\n+5 -2√((n+5)(n-10)) +n-10=1`

Cleaning this up gives you:

`2n-5 -2√((n+5)(n-10))=1`

Now move everything to the other side so we can square this equation again

`-2√((n+5)(n-10))=-2n+6`

Divide both sides by -2

`√((n+5)(n-10))=n-3`

square again

`(n+5)(n-10)=(n-3)^2\\n^2-5n-50=n^2-6n+9`

subtract n^2 from both sides, add 6n, and add 50

`-5n-50=-6n+9\\n-50 = 9\\n=59`

Put this back into the equation and you get a correct answer!

sqrt(59 + 5) = sqrt(64) = 8

sqrt(59-10) = sqrt(49) = 7

8 - 7 = 1