The sum of the squares of two consecutive positive integers is 61.find these two numbers

Question

equations

Answer 1

Hi Marshall;

 

x² + (x+1)² = 61

 

I can see that 5² + 6² = 25+36 = 61

but let's do the algebra

 

x² + x² + 2x + 1 = 61

2x² + 2x - 60 = 0

x² + x - 30 = 0

(x+6)(x-5) = 0

x = -6 or x = 5

 

since we know x is positive then

x = 5

x+1 = 6

Answer 2

Let x = the smaller number

Let x + 1 = the larger number

x² + (x+1)² = 61

x² + x² + 2x + 1 = 61

2X² + 2X - 60 = 0      Divide both sides of the equation by 2.

x² + x - 30 = 0

(x+6)(x-5) = 0

x + 6 = 0    or    x - 5 = 0

x = -6, not positive    x = 5     x+ 1 = 6