The sum of the square of a positive number and the square of 2 more than the number is 52. What is the? number?

Question

I just need the positive number . and other answers for my homework thank you

Answer 1

Let one number = x

Let the other number = x + 2

 

Use these variables to establish appropriate equations.

 

x² + (x + 2)² = 52

 

 

Solve for x from this equation.  Expand any terms to get rid of parentheses.

 

x² + x² + 4x + 4 = 52

 

 

Combine any like terms.

 

2x² + 4x - 48 = 0

 

 

WE now have a quadratic equation. Factor out a 2.

 

2(x² + 2x - 24) = 0

 

 

Factor completely.

 

2(x + 6)(x - 4) = 0

 

 

Set the binomial factors equal to zero.

 

x + 6 = 0              and              x - 4 = 0

 

 

Solve for x from these parts.  Choose the positive x value.

Answer 2

x = the number

 

The given information translates into:

 

x² + (x + 2)² = 52

 

x² + (x² + 4x + 4) = 52

 

2x² + 4x - 48 = 0

 

Divide through by 2 and get

 

x² + 2x - 24 = 0

 

Factor and get

 

(x + 6)(x - 4) = 0

 

The positive number is 4.

Answer 3

Given x is the positive number.

 

x² + (x + 2)² = 52

x² + x² + 4x + 4 = 58

2x² + 4x - 48 = 0 => x² + 2x -24 = 0

 

This can be factored so that (x + 6) * (x - 4) = 0

The solutions are x = -6 or x = 4.

Since x is positive the only possible answer is x = 4.