SOLUTION: Find three consecutive positive on integers such that the sum of the squares of the first and second integers is equal to the square of the third integer -7
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Question 948636: Find three consecutive positive on integers such that the sum of the squares of the first and second integers is equal to the square of the third integer -7 Answer by macston(5194) (Show Source):
You can put this solution on YOUR website! X=first integer; X+2= second integer; X+4=third integer Subtract x^2 from each side Subtract 8X from each side. Subtract 16 from each side.
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=64 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 6, -2.
Here's your graph:
The positive answer is 6 ANSWER: The first integer is 6
Note if not restricted to positive integers, (-2,0,2) also work.
X+2=8 ANSWER 2: The second integer is 8
X+4=10 ANSWER 3: The third integer is 10
CHECK
Sum of the squares of the first two equal square of the third.
