Scroll to see replies
rs=1, \text{ so } s = -1/r \text { and so } r^2+3/r^2 = 4 \implies r^4-4r^2+3 = 0\\[br]\implies r^2 = 1, 3
2z=2\pm\sqrt{4 - 4(1+i)(2\sqrt{3}-2)} \\[br]\implies z = 1 \pm \sqrt{1 - (1+i)(2\sqrt{3}-2)} = 1 \pm \sqrt{3-2\sqrt{3}+2(1-\sqrt{3})i)
F_{k+2}F_k - F_{k+1}^2 \\[br]= (F_{k+1}+F_k)F_k - F_{k+1}^2 \\ [br]= F_k^2 +F_{k+1}F_k - F_{k+1}^2 = F_k^2 - F_{k+1}(F_{k+1} - F_k) \\[br]= [F_{k+1}F_{k-1}+(-1)^{k+1}] - F_{k+1}(F_{k+1} - F_k) \\[br]= (-1)^{k+1} + F_{k+1}F_{k-1} - F_{k+1}(F_{k-1})\\[br]= (-1)^{k+1}F_{k+1}^2
F_{n+k+1} = F_{n+k}+F_{n+k-1}\\[br]= F_kF_{n+1}+F_{k-1}F_n + F_k-1F_{n+1}+F_{k-2}F_n\\[br]=(F_k+F_{k-1})F_{n+1}+(F_{k-1}+F_{k-2}F_n \\[br]=F_{k+1}F_{n+1}+F_k F_n
pr=qs \iff|y+1||y-1| = |x-1||x+1|\\[br]\iff (y+1)^2(y-1)^2 = (x-1)^2(x+1)^2 \\[br]\iff [(y+1)(y-1)]^2 - [(x+1)(x-1)]^2 = 0 \\[br]\iff (y^2-1)^2 - (x^2 - 1)^2 = 0 \\[br]\iff y^4-2y^2 - x^4 + 2x^2 = 0\\[br]\iff y^4-x^4 -2(y^2-x^2) = 0\\[br]\iff (y^2-x^2)[(y^2+x^2)-2] = 0\\[br]\iff (y+x)(y-x)[(y^2+x^2)-2] = 0
pr=qs \iff|y+1||y-1| = |x-1||x+1|\\[br]\iff (y+1)^2(y-1)^2 = (x-1)^2(x+1)^2 \\[br]\iff [(y+1)(y-1)]^2 - [(x+1)(x-1)]^2 = 0 \\[br]\iff (y^2-1)^2 - (x^2 - 1)^2 = 0 \\[br]\iff y^4-2y^2 - x^4 + 2x^2 = 0\\[br]\iff y^4-x^4 -2(y^2-x^2) = 0\\[br]\iff (y^2-x^2)[(y^2+x^2)-2] = 0\\[br]\iff (y+x)(y-x)[(y^2+x^2)-2] = 0
Last reply 4 minutes ago
which unis will accept BBB for economicsLast reply 5 minutes ago
HSBC Degree Apprenticeship 2024Last reply 5 minutes ago
Inlaks, Commonwealth, and Other Scholarships for Indian Students 2024: ThreadLast reply 5 minutes ago
LSE International Social and Public Policy and Economics (LLK1) 2024 ThreadLast reply 6 minutes ago
Official: University of Bristol A100 2024 Entry ApplicantsLast reply 6 minutes ago
shouldn't more and more young people be candidates in local elections now? becauseLast reply 6 minutes ago
Bank of America Degree Apprenticeship 2024Last reply 7 minutes ago
Official London School of Economics and Political Science 2024 Applicant ThreadLast reply 7 minutes ago
Official University of Edinburgh Applicant Thread for 2024Last reply 7 minutes ago
Official: University of Aberdeen A100 2024 Entry ApplicantsLast reply 8 minutes ago
Even Europe’s far-right firebrands seem to sense Brexit is a disaster- The GuardianLast reply 9 minutes ago
TSR Study Together - STEM vs Humanities - Tenth SessionLast reply 12 minutes ago
AQA GCSE Physics Paper 1 (Higher Tier triple) 8463/1H - 22nd May 2024 [Exam Chat]Last reply 12 minutes ago
The Official Funding questions/moans/possible joy ThreadLast reply 15 minutes ago
Government Social Research - Research Officer Scheme 2024Last reply 1 day ago
Edexcel A Level Mathematics Paper 1 (9MA0 01) - 4th June 2024 [Exam Chat]Last reply 4 days ago
Edexcel IGCSE Higher tier Mathematics A Paper 1 1H (4MA1) - 8th November 2023Last reply 1 month ago
Edexcel GCSE Mathematics Paper 3 (1MA1 3) - 13th November 2023 [Exam Chat]Last reply 1 month ago
Edexcel GCSE Statistics Paper 1 Higher Tier (1ST0 1H) - 12th June 2023 [Exam Chat]284
Last reply 1 month ago
Edexcel A Level Mathematics Paper 1 (9MA0 01) - 6th June 2023 [Exam Chat]2960
Last reply 1 month ago
AQA A Level Mathematics Paper 1 (7357/1) - 6th June 2023 [Exam Chat]352
Last reply 1 month ago
Edexcel GCSE Mathematics Paper 2 (1MA1 2) - 10th November 2023 [Exam Chat]Last reply 2 months ago
Edexcel A-level Mathematics Paper 1 [6th June 2023] Unofficial Markscheme156
Last reply 2 months ago
Edexcel GCSE Mathematics Paper 1 (1MA1 1) - 8th November 2023 [Exam Chat]Last reply 3 months ago
Edexcel IGCSE Higher tier Mathematics A Paper 1 1H (4MA1) - 19th May 2023 [Exam Chat]232
Last reply 3 months ago
AQA GCSE Mathematics Paper 3 (Higher) 8300/3H - 14th June 2023 [ Exam Chat]247
Last reply 5 months ago
Edexcel IGCSE Higher tier Mathematics A Paper 2 2H (4MA1) - 10th November 2023Last reply 7 months ago
OCR A-level Mathematics A Paper 3 (H240/03) - 20th June 2023 [Exam Chat]169
Last reply 8 months ago
AQA Level 2 Further Maths 2023 Paper 1 (8365/1) & Paper 2 (8365/2) [Exam Chat]489
Last reply 8 months ago
Edexcel A Level Mathematics Paper 3 (9MA0 03) - 20th June 2023 [Exam Chat]1836
Last reply 8 months ago
AQA A Level Mathematics Paper 3 (7357/3) - 20th June 2023 [Exam Chat]307
Last reply 8 months ago
OCR A-level Mathematics B Paper 3 (H640/03) - 20th June 2023 [Exam Chat]132
Last reply 9 months ago
Edexcel A-level Further Mathematics Paper 1 (9FM0 01) - 25th May 2023 [Exam Chat]902
Last reply 1 day ago
Edexcel A Level Mathematics Paper 1 (9MA0 01) - 4th June 2024 [Exam Chat]Last reply 4 days ago
Edexcel IGCSE Higher tier Mathematics A Paper 1 1H (4MA1) - 8th November 2023Last reply 1 month ago
Edexcel GCSE Mathematics Paper 3 (1MA1 3) - 13th November 2023 [Exam Chat]Last reply 1 month ago
Edexcel GCSE Statistics Paper 1 Higher Tier (1ST0 1H) - 12th June 2023 [Exam Chat]284
Last reply 1 month ago
Edexcel A Level Mathematics Paper 1 (9MA0 01) - 6th June 2023 [Exam Chat]2960
Last reply 1 month ago
AQA A Level Mathematics Paper 1 (7357/1) - 6th June 2023 [Exam Chat]352
Last reply 1 month ago
Edexcel GCSE Mathematics Paper 2 (1MA1 2) - 10th November 2023 [Exam Chat]Last reply 2 months ago
Edexcel A-level Mathematics Paper 1 [6th June 2023] Unofficial Markscheme156
Last reply 2 months ago
Edexcel GCSE Mathematics Paper 1 (1MA1 1) - 8th November 2023 [Exam Chat]Last reply 3 months ago
Edexcel IGCSE Higher tier Mathematics A Paper 1 1H (4MA1) - 19th May 2023 [Exam Chat]232
Last reply 3 months ago
AQA GCSE Mathematics Paper 3 (Higher) 8300/3H - 14th June 2023 [ Exam Chat]247
Last reply 5 months ago
Edexcel IGCSE Higher tier Mathematics A Paper 2 2H (4MA1) - 10th November 2023Last reply 7 months ago
OCR A-level Mathematics A Paper 3 (H240/03) - 20th June 2023 [Exam Chat]169
Last reply 8 months ago
AQA Level 2 Further Maths 2023 Paper 1 (8365/1) & Paper 2 (8365/2) [Exam Chat]489
Last reply 8 months ago
Edexcel A Level Mathematics Paper 3 (9MA0 03) - 20th June 2023 [Exam Chat]1836
Last reply 8 months ago
AQA A Level Mathematics Paper 3 (7357/3) - 20th June 2023 [Exam Chat]307
Last reply 8 months ago
OCR A-level Mathematics B Paper 3 (H640/03) - 20th June 2023 [Exam Chat]132
Last reply 9 months ago
Edexcel A-level Further Mathematics Paper 1 (9FM0 01) - 25th May 2023 [Exam Chat]902