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Category: Algebra

find-the-cubic-of-26-15-3-1-3-26-15-3-1-3-

Question Number 172022 by Mikenice last updated on 23/Jun/22 $${find}\:{the}\:{cubic}\:{of} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}\:\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Jun/22 $${Let}\:\sqrt[{\mathrm{3}}]{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}\:\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}}\:={a} \\ $$$$\:{where}\:{a}\in\mathbb{R} \\…

solve-x-2-5x-2-x-2-5-1-

Question Number 172006 by Mikenice last updated on 23/Jun/22 $${solve}: \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} +\mathrm{5}\:}\:=\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on 24/Jun/22 $$\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}}…

resolve-4-x-4-x-2-2x-3-into-partial-fraction-

Question Number 171999 by Mikenice last updated on 23/Jun/22 $${resolve}: \\ $$$$\frac{\mathrm{4}\left({x}−\mathrm{4}\right)}{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}\:{into}\:{partial}\:{fraction} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Jun/22 $$\frac{\mathrm{4}\left({x}−\mathrm{4}\right)}{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{1}\right)}=\frac{{a}}{{x}−\mathrm{3}}+\frac{{b}}{{x}+\mathrm{1}} \\ $$$$\mathrm{4}\left({x}−\mathrm{4}\right)={a}\left({x}+\mathrm{1}\right)+{b}\left({x}−\mathrm{3}\right)…