# Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

2
Log in to add a comment

Log in to add a comment

The Brainliest Answer!

According to the given condition, we have

x² = [(x +1)² -(x -1)²] +60

x² = (x² +2x +1) -(x² -2x +1) +60 = 4x +60

x² -4x -60 = 0 => (x -10)(x +6) = 0

x = 10 or -6

Since x is a natural number, we get x = 10

Hence the three numbers are 9, 10, 11

=======================================================

There are three consecutive integers (same as, natural numbers).

let the smallest of the numbers be .

1st no. is .

2nd no. is .

3rd no. is .

Since, is an irrational number, so we will not further simplify it.

By putting the values of ,

1st no. is .

2nd no. is .

3rd no. is .

1st no. is .

2nd no. is .

3rd no. is .

-----------------------------------------------------------------------------