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Category: Algebra

Question-132494

Question Number 132494 by mnjuly1970 last updated on 14/Feb/21 Commented by MJS_new last updated on 14/Feb/21 $$\mathrm{sharing}\:\mathrm{these}\:\mathrm{transformations} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{check}\:\mathrm{all}\:\mathrm{solutions}!!! \\ $$$$ \\ $$$${a}^{\mathrm{1}/\mathrm{2}} +{b}^{\mathrm{1}/\mathrm{2}} ={c}^{\mathrm{1}/\mathrm{2}}…

Solve-the-following-compound-inequation-in-interval-0-2pi-tan-x-2-1-and-tan-x-2-lt-0-

Question Number 1418 by Rasheed Ahmad last updated on 04/Aug/15 $${Solve}\:{the}\:{following}\:{compound} \\ $$$${inequation}\:{in}\:{interval}\:\left(\mathrm{0},\:\mathrm{2}\pi\right), \\ $$$${tan}\frac{{x}}{\mathrm{2}}\:\leqslant\:−\mathrm{1}\:\:{and}\:\:{tan}\frac{{x}}{\mathrm{2}}\:<\:\mathrm{0}\:. \\ $$ Commented by 123456 last updated on 31/Jul/15 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{3}\pi}{\mathrm{4}}=\mathrm{tan}\:\frac{\mathrm{5}\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{7}\pi}{\mathrm{4}}=\mathrm{1}…

tan-3-x-dx-

Question Number 132470 by physicstutes last updated on 14/Feb/21 $$\int\:\mathrm{tan}^{\mathrm{3}} {x}\:{dx} \\ $$ Answered by mindispower last updated on 14/Feb/21 $$\int{tg}\left({x}\right)\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({x}\right)\right){dx}−\int{tg}\left({x}\right){dx} \\ $$$$=\frac{{tg}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}}+{ln}\mid{cos}\left({x}\right)\mid+{c}…

8-log-12x-1-4-log-27-solve-for-x-

Question Number 1355 by Rasheed Ahmad last updated on 25/Jul/15 $$\mathrm{8}^{{log}\:\left(\mathrm{12}{x}+\mathrm{1}\right)} =\mathrm{4}^{{log}\:\mathrm{27}} \:\:\:,{solve}\:{for}\:{x}. \\ $$ Answered by Yugi last updated on 25/Jul/15 $${Rewriting}\:{the}\:{above}\:{equation}\:{in}\:{base}\:\mathrm{2}\:{gives} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{3}{log}\left(\mathrm{12}{x}+\mathrm{1}\right)}…