what is photosynthesis
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Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities.
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Let x be any positive integer and y = 3.
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = m
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to get,
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to get,x2= 3m + 1 ………. (2)
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to get,x2= 3m + 1 ………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to get,x2= 3m + 1 ………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1Again, substitute, 3q2+4q+1 = m, to get,
Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m …..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to get,x2= 3m + 1 ………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1Again, substitute, 3q2+4q+1 = m, to get,x2= 3m + 1…………… (3)
Hence, from equation 1, 2 and 3, we can say that, the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.