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solve-x-x-2-1-x-x-2-1-x-x-2-1-x-x-2-1-8x-x-2-3x-2-




Question Number 171873 by Mikenice last updated on 21/Jun/22
solve:  ((x+(√(x^2 −1)))/(x−(√(x^2 −1)))) −((x−(√(x^2 −1)))/(x+(√(x^2 −1))))  =8x(√(x^2 −3x+2))
$${solve}: \\ $$$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:−\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:=\mathrm{8}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$
Commented by infinityaction last updated on 21/Jun/22
3,1
$$\mathrm{3},\mathrm{1} \\ $$
Commented by Mikenice last updated on 21/Jun/22
please sir show the solution
$${please}\:{sir}\:{show}\:{the}\:{solution} \\ $$
Answered by Rasheed.Sindhi last updated on 21/Jun/22
(((x+(√(x^2 −1)))^2 −(x−(√(x^2 −1)))^2 )/(x^2 −x^2 +1))=8x(√(x^2 −3x+2))  4x(√(x^2 −1)) −2x(√(x^2 −3x+2)) =0  x(√((x−1)(x+1))) −2x(√((x−1)(x−2)))  x((√(x−1)) )( (√(x+1)) −2(√(x−2)) )=0  x=0 ∣ x=1 ∣ x+1=4x−8 _(x=3)   x=0 ∣ x=1 ∣ x=3
$$\frac{\left({x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}} −\left({x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} −{x}^{\mathrm{2}} +\mathrm{1}}=\mathrm{8}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$$\mathrm{4}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:−\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}\:=\mathrm{0} \\ $$$${x}\sqrt{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}\:−\mathrm{2}{x}\sqrt{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)} \\ $$$${x}\left(\sqrt{{x}−\mathrm{1}}\:\right)\left(\:\sqrt{{x}+\mathrm{1}}\:−\mathrm{2}\sqrt{{x}−\mathrm{2}}\:\right)=\mathrm{0} \\ $$$${x}=\mathrm{0}\:\mid\:{x}=\mathrm{1}\:\mid\:\underset{{x}=\mathrm{3}} {{x}+\mathrm{1}=\mathrm{4}{x}−\mathrm{8}\:} \\ $$$${x}=\mathrm{0}\:\mid\:{x}=\mathrm{1}\:\mid\:{x}=\mathrm{3} \\ $$
Commented by Mikenice last updated on 23/Jun/22
thanks sir
$${thanks}\:{sir} \\ $$

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