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find-x-2cosh-2x-10sinh-2x-5-




Question Number 140805 by jlewis last updated on 12/May/21
find x 2cosh 2x+10sinh 2x=5
$${find}\:{x}\:\mathrm{2cosh}\:\mathrm{2}{x}+\mathrm{10sinh}\:\mathrm{2}{x}=\mathrm{5} \\ $$
Answered by Ar Brandon last updated on 12/May/21
2cosh2x+10sinh2x=5  e^(2x) +e^(−2x) +5(e^(2x) −e^(−2x) )=5  6e^(2x) −4e^(−2x) −5=0  6e^(4x) −5e^(2x) −4=0  (2e^(2x) +1)(3e^(2x) −4)=0  e^(2x) =(4/3) ⇒x=(1/2)ln((4/3))
$$\mathrm{2cosh2x}+\mathrm{10sinh2x}=\mathrm{5} \\ $$$$\mathrm{e}^{\mathrm{2x}} +\mathrm{e}^{−\mathrm{2x}} +\mathrm{5}\left(\mathrm{e}^{\mathrm{2x}} −\mathrm{e}^{−\mathrm{2x}} \right)=\mathrm{5} \\ $$$$\mathrm{6e}^{\mathrm{2x}} −\mathrm{4e}^{−\mathrm{2x}} −\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{6e}^{\mathrm{4x}} −\mathrm{5e}^{\mathrm{2x}} −\mathrm{4}=\mathrm{0} \\ $$$$\left(\mathrm{2e}^{\mathrm{2x}} +\mathrm{1}\right)\left(\mathrm{3e}^{\mathrm{2x}} −\mathrm{4}\right)=\mathrm{0} \\ $$$$\mathrm{e}^{\mathrm{2x}} =\frac{\mathrm{4}}{\mathrm{3}}\:\Rightarrow\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$
Commented by jlewis last updated on 13/May/21
thanks alot
$${thanks}\:{alot} \\ $$

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