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Category: Algebra

Simplify-x-4-x-4-x-4-x-4-x-8-4-x-2-12x-32-

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

suppose-that-E-9-4-k-2-n-a-k-2-is-given-let-a-k-a-k-1-a-k-1-1-and-a-1-1-a-2-2-a-3-6-

Question Number 198813 by mnjuly1970 last updated on 24/Oct/23 $$ \\ $$$$\:\:\:\:\:{suppose}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:{E}=\:\sqrt{\:\mathrm{9}\:+\:\mathrm{4}\:\left(\:\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\:{a}_{\:{k}} ^{\:\mathrm{2}} \:\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{is}\:\:{given} \\ $$$$\:\:\:\:\:{let}\:\:\:\:{a}_{\:{k}} \:=\:{a}_{{k}−\mathrm{1}}…

x-4-ax-3-bx-2-cx-d-0-

Question Number 198772 by ajfour last updated on 24/Oct/23 $${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$ 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}…

Question-198754

Question Number 198754 by essaad last updated on 24/Oct/23 Answered by Frix last updated on 24/Oct/23 $${x}^{\frac{\mathrm{1}}{\mathrm{2}}} +{x}^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{12} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${x}\approx\mathrm{20}.\mathrm{4490371248} \\ $$…

Question-198644

Question Number 198644 by cortano12 last updated on 22/Oct/23 Commented by Rasheed.Sindhi last updated on 22/Oct/23 $${ab}=\left(\frac{\mathrm{8}−{a}+{b}}{\mathrm{6}}\right)^{\mathrm{3}} \:{or}\:\left(\frac{\mathrm{8}+{a}−{b}}{\mathrm{6}}\right)^{\mathrm{3}} \:? \\ $$ Commented by cortano12 last…

Question-198647

Question Number 198647 by ajfour last updated on 22/Oct/23 Commented by ajfour last updated on 22/Oct/23 $${Q}\:{is}\:{center}\:{of}\:{smaller}\:{circle}\:{of} \\ $$$${radius}\:{a}.\:{Find}\:{maximum}\:{area}\:{of}\: \\ $$$$\bigtriangleup{ABC}\:\:{in}\:{terms}\:{of}\:{a},\:{b}. \\ $$ Answered by…