Question Number 114668 by bemath last updated on 20/Sep/20
$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:+\:\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\mathrm{98}\: \\ $$
Answered by som(math1967) last updated on 20/Sep/20
$$\frac{\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}} +\left(\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\left(\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}} }=\mathrm{98} \\ $$$$\Rightarrow\frac{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}{\mathrm{1}}=\mathrm{98} \\ $$$$\Rightarrow\mathrm{2x}^{\mathrm{2}} −\mathrm{1}=\mathrm{49} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} =\frac{\mathrm{50}}{\mathrm{2}} \\ $$$$\mathrm{x}=\pm\mathrm{5}\:\mathrm{ans} \\ $$$$ \\ $$
Commented by bemath last updated on 20/Sep/20
$${gave}\:{kudos}\: \\ $$
Commented by som(math1967) last updated on 20/Sep/20
$$\mathrm{Is}\:\mathrm{the}\:\mathrm{langage}\:\mathrm{from}\:\mathrm{Indonesia}? \\ $$
Commented by bemath last updated on 21/Sep/20
$${no}\:{sir} \\ $$