Question Number 12265 by frank ntulah last updated on 17/Apr/17 $${Determinant}\:{method}\:{can}\:{be}\:{used}\:{to}\:{solve} \\ $$$${the}\:{system}\:{below}?,\:\mathrm{if}\:\mathrm{yes}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{determinant}\:\mathrm{method}\:\mathrm{and} \\ $$$$\:\mathrm{if}\:\mathrm{no}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{another}\:\mathrm{method} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$${x}+{y}−{z}=\mathrm{8} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{3} \\ $$$$\left({give}\:{clear}\:{reason}\:{for}\:{your}\:{answer}\right) \\ $$…
Question Number 143332 by bramlexs22 last updated on 13/Jun/21 Commented by soumyasaha last updated on 13/Jun/21 $$\:\mathrm{x}\:=\:\sqrt{\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}} \\ $$ Commented by mr W last updated…
Question Number 77799 by mr W last updated on 10/Jan/20 $${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$ Answered by mr…
Question Number 12261 by frank ntulah last updated on 17/Apr/17 $${find}\:{the}\:{value}\:{of}\:{a}\:{b}\:{and}\:{c} \\ $$$$\:{a}+{b}+{c}=\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{66} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{280} \\ $$…
Question Number 143329 by Huy last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2x}+\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{\mathrm{x}+\mathrm{1}} \left(\mathrm{3}\sqrt{\mathrm{2x}+\mathrm{5}}+\mathrm{18}\right)=\mathrm{2x} \\ $$ Answered by Olaf_Thorendsen last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2}{x}+\mathrm{1}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{{x}+\mathrm{1}}…
Question Number 143328 by Rankut last updated on 13/Jun/21 $${x}+\sqrt{{xy}}+{y}=\mathrm{14}\:\:{and}\: \\ $$$${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\mathrm{84}\:, \\ $$$${find}\:{x}\:{and}\:{y} \\ $$ Answered by Rasheed.Sindhi last updated on 13/Jun/21…
Question Number 12257 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by sma3l2996 last updated on 17/Apr/17 $$\left({a}+{b}−\mathrm{2}{ab}\right)^{\mathrm{2}} +\left({a}+{b}−\mathrm{1}\right)^{\mathrm{2}} =\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{4}{a}^{\mathrm{2}} {b}^{\mathrm{2}} −\mathrm{4}{ab}^{\mathrm{2}} +\mathrm{2}{a}\left({b}−\mathrm{2}{ab}\right)\right)+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 77790 by aliesam last updated on 10/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{−{log}\left({x}\right)}}\:{dx} \\ $$ Answered by MJS last updated on 10/Jan/20 $$\int\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\:\rightarrow\:{dx}=−\mathrm{2}{x}\sqrt{−\mathrm{ln}\:{x}}{dt}\right] \\…
Question Number 12255 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by mrW1 last updated on 16/Apr/17 $$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{4}\right)+\mathrm{1} \\ $$$$=\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{3}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}\right)+\mathrm{1} \\ $$$$=\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \right]\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \right]+\mathrm{1}…
Question Number 143324 by Rankut last updated on 13/Jun/21 $$\left(\boldsymbol{{x}}^{\mathrm{2}\boldsymbol{{x}}^{−\frac{\mathrm{1}}{\mathrm{5}}} } \right)^{−\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{25}} \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\:\boldsymbol{\mathrm{x}} \\ $$ Answered by gsk2684 last updated on 13/Jun/21 $$\mathrm{x}^{\mathrm{2x}^{−\frac{\mathrm{1}}{\mathrm{5}}}…