SOLUTION: Prove that (5,x,x+1)are Pythagorean triplets

Question 1133609: Prove that (5,x,x+1)are Pythagorean triplets
Found 3 solutions by MathLover1, Alan3354, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

(,,) are Pythagorean triplets if
find such that:

(,,)=(,,)

=> proof that (,,) are Pythagorean triplets

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Prove that (5,x,x+1)are Pythagorean triplets
==============
x = 2
5-2-3 is not a right triangle.
Disproven.
**************************
If you meant to find x such that it's a right triangle, you should have said that.
==========================
5^2 = 25
25/2 = 12.5 --> 12 & 13
5-12-13 is a right triangle.
**************
3-4-5 is also a solution.
3^2 = 9
9/2 = 4.5 --> 4 & 5
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In the same manner:
7^2 = 49
49/2 = 24.5 --> 7-24-25

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Prove that (5,x,x+1)are Pythagorean triplets

x CANNOT be the longest side (hypotenuse) since it's smaller than x + 1
Therefore, using x + 1 as hypotenuse, you'll get the following equation: , and the pythagorean triple: 5-12-13.
Using 5 as the hypotenuse, you'll get the following equation: , and the pythagorean triple: 3-4-5, when the POSITIVE (> 0) value of x is chosen.
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