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Category: Algebra

Question-11813

Question Number 11813 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17 Commented by mrW1 last updated on 01/Apr/17 $${depending}\:{on}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b}, \\ $$$${there}\:{are}\:\mathrm{5}\:{cases}: \\ $$$$\left.\mathrm{1}\right)\:{no}\:{solution} \\ $$$$\left.\mathrm{2}\right)\:{one}\:{solution} \\ $$$$\left.\mathrm{3}\right)\:{two}\:{solutions}…

Question-77340

Question Number 77340 by BK last updated on 05/Jan/20 Answered by mind is power last updated on 05/Jan/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{3}} +\mathrm{t}^{\mathrm{2}} +\mathrm{16t}+\mathrm{60} \\ $$$$\mathrm{z}=\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{y}=\mathrm{fof}\left(\mathrm{x}\right)…

Let-a-1-a-2-a-3-be-an-arithmethic-progression-of-positive-real-numbers-Then-1-a-1-a-2-1-a-2-a-3-1-a-n-1-a-n-A-n-1-a-1-a-n-

Question Number 142865 by EnterUsername last updated on 06/Jun/21 $$\mathrm{Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:…\:\mathrm{be}\:\mathrm{an}\:\mathrm{arithmethic}\:\mathrm{progression}\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}.\:\mathrm{Then} \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{1}}{\:\sqrt{{a}_{\mathrm{1}} }+\sqrt{{a}_{\mathrm{2}} }}+\frac{\mathrm{1}}{\:\sqrt{{a}_{\mathrm{2}} }+\sqrt{{a}_{\mathrm{3}} }}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\:\sqrt{{a}_{{n}−\mathrm{1}} }+\sqrt{{a}_{{n}} }}= \\ $$$$\left(\mathrm{A}\right)\:\frac{{n}+\mathrm{1}}{\:\sqrt{{a}_{\mathrm{1}}…

x-y-z-1-x-2-y-2-z-2-2-x-3-y-3-z-3-3-find-x-8-y-8-z-8-

Question Number 77313 by David Danile last updated on 05/Jan/20 $$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{3} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{8}}…

if-x-y-and-z-are-solution-of-x-xy-x-y-1-2-2x-xz-x-z-2-3-2-2y-z-yz-y-z-3-4-so-the-value-of-1-x-1-y-1-1-z-2-

Question Number 11764 by Peter last updated on 31/Mar/17 $$\mathrm{if}\:\mathrm{x}\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\mathrm{are}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\frac{\mathrm{x}\:+\:\mathrm{xy}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{2} \\ $$$$\frac{\mathrm{2x}\:+\:\mathrm{xz}}{\mathrm{x}\:+\:\mathrm{z}\:+\mathrm{2}}\:=\:\mathrm{3} \\ $$$$\frac{\mathrm{2}\:+\:\mathrm{2y}+\:\mathrm{z}\:+\:\mathrm{yz}}{\mathrm{y}\:+\:\mathrm{z}\:+\mathrm{3}}\:=\:\mathrm{4} \\ $$$$\mathrm{so},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{z}\:+\:\mathrm{2}\:}\:=\:….? \\ $$$$ \\ $$ Answered…

1-sin2x-dx-

Question Number 11766 by uni last updated on 31/Mar/17 $$\int\frac{\mathrm{1}}{\mathrm{sin2x}}\mathrm{dx}=? \\ $$ Answered by ajfour last updated on 31/Mar/17 $$\int\:\frac{{dx}}{\mathrm{2sin}\:{x}\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} {x}}{\mathrm{tan}\:{x}}\:{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{tan}\:{x}\mid+{C} \\ $$…