# Numbers.The sum of the squares of two consecutive real numbers is 61. Find the numbers.

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### 1 Answer

Let x and x+1 be the two consecutive numbers. We know, from enunciation that the sum of their squares is 61:

x^2 + (x+1)^2 = 61

We'll expand the square using the formula:

(a+b)^2 = a^2 + 2ab + b^2

We'll put a = x and b = 1:

x^2 + x^2 + 2x + 1 = 61

We'll combine like terms and we'll get:

2x^2 + 2x - 60 = 0

We'll divide by 2:

x^2 + x - 30 = 0

We'll apply the quadratic formula:

x1 = [-1+sqrt(1 + 120)]/2

x1 = (-1+11)/2

x1 = 5

x2 = -6

The first solution for the given problem is:

x = 5 => x+1 = 5+1 = 6

The 2 consecutive numbers whose sum of the squares is 61 are: 5,6.

5^2 + 6^2 = 25 + 36 = 61

The secondsolution for the given problem is:

x = -6 => x+1 = -6+1 = -5

The 2 consecutive numbers whose sum of the squares is 61 are: -6,-5.

(-6)^2 + (-5)^2= 61