दिखाइए कि किसी भी धन पूर्णांक का वर्ग 6m+2 या 6m+5 के रूप का नहीं हो सकता, जहाँ m कोई पूर्णांक है if you know the answer so just then answer it otherwise don't
Answers
Given : धन पूर्णांक का वर्ग
Square of positive integer
To Find : दिखाइए कि धन पूर्णांक का वर्ग 6m+2 या 6m+5 रे रूप का नहीं हो सकता
Square of any positive integer can not be of form 6m + 2or 6m + 5
Solution:
Without losing generality any number can be Written in the form
6k , 6k+1 , 6k+2 , 6k+3 , 6k+4 , 6k + 5
(6k)² = 36k² = 6* 6k² = 6m
(6k + 1)² = 36k² + 12k + 1 = 6(6k² + 2k) + 1 = 6m + 1
(6k + 2)² = 36k² + 24k + 4 = 6(6k² +4k) +4 = 6m + 4
(6k + 3)² = 36k² + 36k + 9 = 6(6k² + 6k+1) + 3 = 6m + 3
(6k + 4)² = 36k² + 48k + 16 = 6(6k² +8k + 2) +4 = 6m + 4
(6k + 5)² = 36k² + 60k + 25 = 6(6k² +10k + 4) +1 = 6m + 1
Hence we can notice that square of any positive integer is of form
6m , 6m+ 1 , 6m+3 , 6m+4 only
Hence
Square of any positive integer can not be of form 6m + 2or 6m + 5
किसी भी धन पूर्णांक का वर्ग 6m+2 या 6m+5 रे रूप का नहीं हो सकता
Learn More:
prove that square of any positive integer is of the form 9k or 9k+1 ...
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Prove that square of any positive even integer is always even ...
brainly.in/question/7353545
Answer:
Given : धन पूर्णांक का वर्ग
Square of positive integer
To Find : दिखाइए कि धन पूर्णांक का वर्ग 6m+2 या 6m+5 रे रूप का नहीं हो सकता
Square of any positive integer can not be of form 6m + 2or 6m + 5
Solution:
Without losing generality any number can be Written in the form
6k , 6k+1 , 6k+2 , 6k+3 , 6k+4 , 6k + 5
(6k)² = 36k² = 6* 6k² = 6m
(6k + 1)² = 36k² + 12k + 1 = 6(6k² + 2k) + 1 = 6m + 1
(6k + 2)² = 36k² + 24k + 4 = 6(6k² +4k) +4 = 6m + 4
(6k + 3)² = 36k² + 36k + 9 = 6(6k² + 6k+1) + 3 = 6m + 3
(6k + 4)² = 36k² + 48k + 16 = 6(6k² +8k + 2) +4 = 6m + 4
(6k + 5)² = 36k² + 60k + 25 = 6(6k² +10k + 4) +1 = 6m + 1
Hence we can notice that square of any positive integer is of form
6m , 6m+ 1 , 6m+3 , 6m+4 only
Hence
Square of any positive integer can not be of form 6m + 2or 6m + 5
किसी भी धन पूर्णांक का वर्ग 6m+2 या 6m+5 रे रूप का नहीं हो सकता
Learn More:
prove that square of any positive integer is of the form 9k or 9k+1 ...
brainly.in/question/20017920
Prove that square of any positive even integer is always even ...
brainly.in/question/7353545