Question

Find the other two numbers of the pythagorean triplets, one of whose number is :
a) 10
b) 26

Answer 1

Answer:

Answer is 24.

Step-by-step explanation:

6 and 8. 6² + 8² = 10². You can find that by trial and error: if a²+b² = 100, then one of a² and b² must lie between 50 and 99, and there are only two perfect squares, viz. 8² and 9², in that range; so just subtract them from 10² and see if the difference happens to also be a perfect square. (I am ignoring the trivial solution 10² + 0² = 10².)

Also, 26 and 24. 26² = 24² + 10².

To find this second solution, consider the equation x² = 10² + y². Transform it into 100 = (x+y)(x-y). Now x+y and x-y must either be both even or both odd, since their sum 2x is even; but as their product, 100, is even, at least one of them must be even; so they are both even. Thus we must express 100 as the product of two even numbers. These can only be 50 and 2 (or 10 and 10, which yields the trivial solution x=10, y=0). Then x = ½(50+2) = 26 and y = ½(50–2) = 24.

There are no other solutions.