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MATH Solutions By PHANI
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#👩💻టెట్/DSC ప్రత్యేకం
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![👩💻టెట్/DSC ప్రత్యేకం - Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_200099_31576703_1768802198814_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=814_sc.jpg "👩💻టెట్/DSC ప్రత్యేకం - Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) - ShareChat")