Write a Pythagoreantriplet whose one member is
(i) 6 (ii) 14
(iii) 16 (iv) 18
Write a Pythagoreantriplet whose one member is
(i) 6 (ii) 14
(iii) 16 (iv) 18
For any natural number m >1, 2m, m2 − 1, m2 +1 forms a Pythagorean triplet.
(i) If we take m2+ 1 = 6, then m2 = 5
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 6, then m2= 7
Againthe value of m is not an integer.
Let2m = 6
m= 3
Therefore,the Pythagorean triplets are 2 × 3, 32 − 1, 32+ 1 or 6, 8, and 10.
(ii) If we take m2+ 1 = 14, then m2 = 13
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 14, then m2= 15
Againthe value of m is not an integer.
Let2m = 14
m= 7
Thus,m2 − 1 = 49 − 1 = 48 and m2+ 1 = 49 + 1 = 50
Therefore,the required triplet is 14, 48, and 50.
(iii) If we take m2+ 1 = 16, then m2 = 15
Thevalue of m will not be an integer.
Ifwe take m2 − 1= 16, then m2= 17
Againthe value of m is not an integer.
Let2m = 16
m= 8
Thus,m2 − 1 = 64 − 1 = 63 and m2+ 1 = 64 + 1 = 65
Therefore,the Pythagorean triplet is 16, 63, and 65.
(iv) If we take m2+ 1 = 18,
m2= 17
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 18, then m2= 19
Againthe value of m is not an integer.
Let2m =18
m= 9
Thus,m2 − 1 = 81 − 1 = 80 and m2+ 1 = 81 + 1 = 82
Therefore,the Pythagorean triplet is 18, 80, and 82.
For any natural number m >1, 2m, m2 − 1, m2 +1 forms a Pythagorean triplet.
(i) If we take m2+ 1 = 6, then m2 = 5
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 6, then m2= 7
Againthe value of m is not an integer.
Let2m = 6
m= 3
Therefore,the Pythagorean triplets are 2 × 3, 32 − 1, 32+ 1 or 6, 8, and 10.
(ii) If we take m2+ 1 = 14, then m2 = 13
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 14, then m2= 15
Againthe value of m is not an integer.
Let2m = 14
m= 7
Thus,m2 − 1 = 49 − 1 = 48 and m2+ 1 = 49 + 1 = 50
Therefore,the required triplet is 14, 48, and 50.
(iii) If we take m2+ 1 = 16, then m2 = 15
Thevalue of m will not be an integer.
Ifwe take m2 − 1= 16, then m2= 17
Againthe value of m is not an integer.
Let2m = 16
m= 8
Thus,m2 − 1 = 64 − 1 = 63 and m2+ 1 = 64 + 1 = 65
Therefore,the Pythagorean triplet is 16, 63, and 65.
(iv) If we take m2+ 1 = 18,
m2= 17
Thevalue of m will not be an integer.
Ifwe take m2 − 1 = 18, then m2= 19
Againthe value of m is not an integer.
Let2m =18
m= 9
Thus,m2 − 1 = 81 − 1 = 80 and m2+ 1 = 81 + 1 = 82
Therefore,the Pythagorean triplet is 18, 80, and 82.
