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Category: Algebra

solve-in-R-8-x-4-1-5-x-3-1-7x-2-12-

Question Number 91872 by  M±th+et+s last updated on 03/May/20 $${solve}\:{in}\:\mathbb{R} \\ $$$$\mathrm{8}\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}+\mathrm{5}\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}=\mathrm{7x}^{\mathrm{2}} +\mathrm{12} \\ $$ Commented by MJS last updated on 03/May/20 $$\mathrm{you}\:\mathrm{can}\:\begin{cases}{\left(\mathrm{square}+\mathrm{transform}\right)×\mathrm{2}\:\mathrm{and}\:\mathrm{then}}\\{\:\:\:\:\:\mathrm{approximate}\:\mathrm{the}\:\mathrm{8}^{\mathrm{th}}…

1-x-2x-x-4x-6-x-0-x-

Question Number 91870 by hmamarques1994@gmail.com last updated on 03/May/20 $$\:\frac{\overset{\:} {\mathrm{1}}}{\mathrm{x}^{\mathrm{2x}} }\:+\:\mathrm{x}^{−\mathrm{4x}} \:=\:\mathrm{6},\:\:\left(\mathrm{x}\:\neq\:\mathrm{0}\right) \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\underset{\:} {?} \\ $$ Commented by MJS last updated…

Prove-by-mathematical-induction-r-1-n-1-r-r-1-n-n-1-

Question Number 157351 by physicstutes last updated on 22/Oct/21 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\left({r}+\mathrm{1}\right)}\:=\:\frac{{n}}{{n}+\mathrm{1}} \\ $$ Commented by hknkrc46 last updated on 22/Oct/21 $$\bigstar\:\frac{\mathrm{1}}{\boldsymbol{{r}}\left(\boldsymbol{{r}}\:+\:\mathrm{1}\right)}\:=\:\frac{\left(\boldsymbol{{r}}\:+\:\mathrm{1}\right)\:−\:\boldsymbol{{r}}}{\boldsymbol{{r}}\left(\boldsymbol{{r}}\:+\:\mathrm{1}\right)} \\…