A. Write an equation representing the fact that the sum of the squares of two consecutive integers is 113

Question

***2nd part to question: solve the equation from part a to find the two integers***

a. Write an equation in terms of x that represents the given relationship

b. Solve the equation to find the dimensions of the given shape

Answer 1

Part A:

Let x be the first integer

And x+1 be the second integer

Step 1:

The question is saying the sum of square of this two integers will be 113. So the equation will be:

x²⁺(x+1)²=113

Step 2:

Expand the equation

x²+(x+1)² ----> x²+ (x+1)(x+1)----> x²+(x²+2x+1)---->2x²+2x+1

2x²+2x+1=113

Part B:

You will need to use the quadratic equation to solve it.

2x²+2x+1=113 ----> 2x²+2x-112=0

(I can not put the equation here)

The values of x will be 8 and -7, but since the question is asking for the dimensions of a shape, -7 can't exist so the value of x will be 8, and the other integer will be 8+1 =9