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Question-69393




Question Number 69393 by 06 last updated on 23/Sep/19
Commented by Prithwish sen last updated on 23/Sep/19
(3^t +3^(−t) )^3 = 5^3 ⇒27^t +27^(−t) +3.3^t .3^(−t) (3^t +3^(−t) )=125  ⇒27^t +27^(−t) +3.5=125 (by putting 3^t +3^(−t) =5)  ⇒27^t +27^(−t) = 110
$$\left(\mathrm{3}^{\mathrm{t}} +\mathrm{3}^{−\mathrm{t}} \right)^{\mathrm{3}} =\:\mathrm{5}^{\mathrm{3}} \Rightarrow\mathrm{27}^{\mathrm{t}} +\mathrm{27}^{−\mathrm{t}} +\mathrm{3}.\mathrm{3}^{\mathrm{t}} .\mathrm{3}^{−\mathrm{t}} \left(\mathrm{3}^{\mathrm{t}} +\mathrm{3}^{−\mathrm{t}} \right)=\mathrm{125} \\ $$$$\Rightarrow\mathrm{27}^{\mathrm{t}} +\mathrm{27}^{−\mathrm{t}} +\mathrm{3}.\mathrm{5}=\mathrm{125}\:\left(\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{putting}}\:\mathrm{3}^{\boldsymbol{\mathrm{t}}} +\mathrm{3}^{−\boldsymbol{\mathrm{t}}} =\mathrm{5}\right) \\ $$$$\Rightarrow\mathrm{27}^{\boldsymbol{\mathrm{t}}} +\mathrm{27}^{−\boldsymbol{\mathrm{t}}} =\:\mathrm{110}\: \\ $$
Commented by 06 last updated on 28/Sep/19
Thank you
$$\mathrm{Thank}\:\mathrm{you} \\ $$

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