QNO 1: Three integers a, b and c with a<b<c , are said toform a Pythagores Tripl

Question

QNO 1: Three integers a, b and c with a<b<c , are said toform a Pythagores Triple if c 2= a 2+b 2 For example 3, 4, 5 form a Pythagorean Triplebecause. 3 2+4 2 =9+16=25=>52 a) Form a Pythagorean Triple i) in which the first two integers are 12 and 16 ii)in which the last integer is 25 b) i)Simplify (3n)2 + (4n)2 . ii) Hence form a Pythagorean Triple in which the last integeris 35. c) Consider 1+2n+n2 =(1+n)2 if 1+2n is a perfect square, say 1+2n = k2 we havek2+n2 =(1+n)2 then K, n, 1+n is a pythagorean Triple for eg when n =12, 1+2n=25=52 and then 5, 12, 13 form a Pythagorean Triple. i) in the same way find the corresponding pythagorean Triplewhen n=24 ii) can we get a Pythagoran Triple in the same way when 1+2n42 ? Why? iii) Form a Pythagorean Triple such that the first integer is9 and the other two integers differ by 1. QNO 1: Three integers a, b and c with a<b<c , are said toform a Pythagores Triple if c 2= a 2+b 2 For example 3, 4, 5 form a Pythagorean Triplebecause. 3 2+4 2 =9+16=25=>52 a) Form a Pythagorean Triple i) in which the first two integers are 12 and 16 ii)in which the last integer is 25 b) i)Simplify (3n)2 + (4n)2 . ii) Hence form a Pythagorean Triple in which the last integeris 35. c) Consider 1+2n+n2 =(1+n)2 if 1+2n is a perfect square, say 1+2n = k2 we havek2+n2 =(1+n)2 then K, n, 1+n is a pythagorean Triple for eg when n =12, 1+2n=25=52 and then 5, 12, 13 form a Pythagorean Triple. i) in the same way find the corresponding pythagorean Triplewhen n=24 ii) can we get a Pythagoran Triple in the same way when 1+2n42 ? Why? iii) Form a Pythagorean Triple such that the first integer is9 and the other two integers differ by 1. and then 5, 12, 13 form a Pythagorean Triple. i) in the same way find the corresponding pythagorean Triplewhen n=24 ii) can we get a Pythagoran Triple in the same way when 1+2n42 ? Why? iii) Form a Pythagorean Triple such that the first integer is9 and the other two integers differ by 1.

Explanation / Answer

a) i) a=12, b= 16, c= (12*12+ 16+16) c=20 ii) c= 25, therefore, a=15 b=20 or a=7 b=24 b) i) 25 n2 ii)n=7 c) i)k=7, a=7,b=24.c=25 ii) NO, then n is not an integer iii) k=9, n=40, k,n,n+1 ==> 9,40,41

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