Category: Algebra

Question Number 198902 by necx122 last updated on 25/Oct/23 $$Giventhat{k}^2-3k+5=0,determine$$$$thevalueof{k}^4-6k^3+9k^2-7$$ Answered by witcher3 last updated on 25/Oct/23…

Question Number 198932 by necx122 last updated on 25/Oct/23 $$Findthevalueofmgiventhatthe$$$$rootsof{x}^4-15x^3+70x^2-120x+m=0$$$$formageometricprogression.$$ Answered by AST last updated on…

Question Number 198919 by necx122 last updated on 25/Oct/23 $$Findthesumofthefourthpowersof$$$$therootsofequation:$$$$7x^3-21x^2+9x+2=0$$ Commented by necx122 last updated on 25/Oct/23…

Question Number 198814 by hardmath last updated on 24/Oct/23 $$\mathrm{Simplify}:$$$$\frac{(\sqrt{\mathrm{x}+4\sqrt{\mathrm{x}-4}}+\sqrt{\mathrm{x}-4\sqrt{\mathrm{x}-4}})\sqrt{\mathrm{x}-8}}{4\sqrt{{\mathrm{x}}^2-12\mathrm{x}+32}}$$ Answered by a.lgnaoui last updated on 24/Oct/23 $$=\frac{1}{4}\sqrt{\frac{\mathrm{x}+4\sqrt{\mathbf{x}-4}}{\mathbf{x}-4}}+\frac{1}{4}\sqrt{\frac{\mathbf{x}-\sqrt{\mathbf{x}-4}}{\mathbf{x}-4}}$$$$=\frac{\sqrt{\boldsymbol{\mathrm{x}}+\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}\:}\:+\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}}{\:\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}…

Question Number 198772 by ajfour last updated on 24/Oct/23 $$x^4+{ax}^3+{bx}^2+cx+d=0$$ Commented by Frix last updated on 24/Oct/23 $$\mathrm{Usually}\mathrm{we}\mathrm{first}\mathrm{try}\mathrm{factors}\mathrm{of}d.\mathrm{The}\mathrm{next}$$$$\mathrm{step}\:\mathrm{would}\:\mathrm{be}\:\mathrm{substituting}\:{x}={t}−\frac{{a}}{\mathrm{4}}\:\mathrm{to}…