Question

If p,q are two consecutive odd numbers and p+q,pq,x are pythagorean triple then the value of x is

Answer 1

Step-by-step explanation:

x is

..

17

hope it helps you

Answer 2

The value of x can be 17,37,65,101,... etc

• p and q are two consecutive odd numbers. Hence q = p+2
• Now it is given that p+q , pq and x are pythagorean triples. Hence this trio follows pythagorean theorem
• Hence  $(p+q)^{2} +(pq)^{2} =x^{2}$ . Now putting the value of q we get $(2p+2)^{2} +(p^{2}+2p) ^{2} =x^{2}$
• Simplifying it we get $p^{4} +4p^{3} +8p^{2}+8p+4 = x^{2}$
• Square rooting both sides we get x = $p^{2} +2p+2$
• Now this yields to numerous values of x. As p is an odd p number  putting p = 3,5,7,9 etc we get x = 17,37,65,101 etc