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Category: Algebra

x-x-100-find-x-

Question Number 16906 by tawa tawa last updated on 28/Jun/17 $$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{100},\:\mathrm{find}\:\mathrm{x}. \\ $$ Answered by mrW1 last updated on 28/Jun/17 $$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{100} \\ $$$$\mathrm{x}=\mathrm{100}^{\frac{\mathrm{1}}{\mathrm{x}}}…

3x-2-7-x-m-5-0-At-what-value-of-m-can-the-equation-have-three-roots-

Question Number 147978 by mathdanisur last updated on 24/Jul/21 $$\mathrm{3}{x}^{\mathrm{2}} \:-\:\mathrm{7}\:\mid{x}\mid\:+\:{m}\:-\:\mathrm{5}\:=\:\mathrm{0}\: \\ $$$${At}\:{what}\:{value}\:{of}\:\boldsymbol{{m}}\:{can}\:{the}\:{equation} \\ $$$${have}\:{three}\:{roots} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{In}\:\mathbb{R},\:\mathrm{the}\:\mathrm{equation}\:\mathrm{can}\:\mathrm{have}\:\mathrm{two}…

The-quadratic-polynomials-p-x-a-x-3-2-bx-1-and-q-x-2x-2-c-x-2-13-are-equal-for-all-values-of-x-Find-the-values-of-a-b-and-c-

Question Number 16881 by Tinkutara last updated on 27/Jun/17 $$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{polynomials} \\ $$$${p}\left({x}\right)\:=\:{a}\left({x}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:+\:{bx}\:+\:\mathrm{1}\:\mathrm{and} \\ $$$${q}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:+\:{c}\left({x}\:−\:\mathrm{2}\right)\:+\:\mathrm{13}\:\mathrm{are}\:\mathrm{equal} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:{x}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a}, \\ $$$${b},\:\mathrm{and}\:{c}. \\ $$ Answered by RasheedSoomro…

x-2-6x-3-0-2x-2-3-6-x-2-

Question Number 147941 by mathdanisur last updated on 24/Jul/21 $${x}^{\mathrm{2}} \:-\:\mathrm{6}{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:\:\:\Rightarrow\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{3}}\:+\:\frac{\mathrm{6}}{{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 24/Jul/21 $${x}^{\mathrm{2}} \:-\:\mathrm{6}{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\Rightarrow{x}^{\mathrm{2}} =\mathrm{6}{x}−\mathrm{3}…

x-2-x-2-x-1-

Question Number 147943 by mathdanisur last updated on 24/Jul/21 $$\int\:\frac{\left({x}^{\mathrm{2}} \:+\:{x}\right)^{\mathrm{2}} }{{x}\:+\:\mathrm{1}}\:=\:? \\ $$ Commented by tabata last updated on 24/Jul/21 $$=\int\:\frac{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\left({x}+\mathrm{1}\right)}{dx}=\int\:{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right){dx}=\frac{{x}^{\mathrm{4}}…