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