Find the pythagareem triplets whose smallest number is 7
Answers
hey mate
As we know 2m, m 2 + 1 and m2 - 1 form a Pythagorean triplet for any number, m > 1.we know that m 2 + 1 >m2 - 1but we don't know what is greater between m2 - 1 & 2m.So, let us assume that 2m =7.Answer will be in decimals....let us assume that m2 - 1=7m2 =8Again a problem. So, I tried hit and trial method and got:(25)2 = (24)2 +(7)2625 = 576 +49.And that's the answer you REQUIRED.2nd Hit and trial method :Actually, 2mn, n 2 + m 2 and n2 - m2 form a Pythagorean triplet .So, in the first case we took n2 -1 =7now, we will take n2- m2=7n2 = 7+m2hence we conclud that 7+m2 should be a perfect square so as to make n an integer, On trials when m=37+m2 =16, a perfect square ,n=42mn=24,n 2 + m 2=25n2 - m2=7Hence we got the answer. Hope it helps.
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