Find all integers?

Question

Find all 2-digit integers x for which sqrt(x+x^2) is an integer.

Answer 1

There are no two-digit numbers, an integer and the succeeding integer, for which your situation would ever be true

Answer 2

Think about what you are asking here...
= sqrt ( x + x² )
= sqrt ( x (x + 1) )

So you are multiplying an integer and the next consecutive integer. As long as x is greater than zero, the square root will always be between the two integers, thus never an integer itself. in fact, as x increases, you get closer and closer to x + ½, so it will never be an integer.

The answer is there are no 2-digit integers with this property.

Answer 3

There are none, sqrt((x+1)x) is never an integer, unless x=0.

Answer 4

There are none

Answer 5

idk good luck