Question Number 187613 by mustafazaheen last updated on 19/Feb/23
$${how}\:{is}\:{solution} \\ $$$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{13}} =\mathrm{x}\:\:\:\:\:\:\:\:\:\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{221}} =? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{x}^{−\mathrm{16}} \left.\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{x}^{−\mathrm{17}} \:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{x}^{\mathrm{221}} \:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{x}^{\mathrm{21}} \\ $$
Commented by a.lgnaoui last updated on 19/Feb/23
$$\left.\mathrm{2}\right)\mathrm{x}^{−\mathrm{17}} \\ $$
Answered by SEKRET last updated on 19/Feb/23
$$\:\:\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{13}} }\:=\:\boldsymbol{\mathrm{x}}\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{2}\:}\:+\mathrm{1}=\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{13}}]{\boldsymbol{\mathrm{x}}}} \\ $$$$\:\:?=\left(\sqrt[{\mathrm{13}}]{\boldsymbol{\mathrm{x}}}\:\right)^{−\mathrm{221}} =\boldsymbol{\mathrm{x}}^{−\mathrm{17}} \\ $$
Answered by a.lgnaoui last updated on 19/Feb/23
$$\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)^{\mathrm{13}} ={x} \\ $$$$\sqrt{\mathrm{2}}\:−\mathrm{1}={x}^{\frac{\mathrm{1}}{\mathrm{13}}} \\ $$$$\left(\sqrt{\mathrm{2}\:}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)=\mathrm{1} \\ $$$$\left(\sqrt{\mathrm{2}}\:+\mathrm{1}\right)^{\mathrm{221}} ×\left(\sqrt{\mathrm{2}\:}\:−\mathrm{1}\right)^{\mathrm{221}} =\mathrm{1} \\ $$$$\Rightarrow\left(\sqrt{\mathrm{2}}\:+\mathrm{1}\right)^{\mathrm{221}} =\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)^{−\mathrm{221}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left({x}^{\frac{\mathrm{1}}{\mathrm{13}}} \right)^{−\mathrm{221}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={x}^{\frac{−\mathrm{221}}{\mathrm{13}}} \\ $$$$\:\:\:{Reponse}\::\left(\mathrm{2}\right)\:=\:\:\:{x}^{−\mathrm{17}} \\ $$$${this}\:{is}\:{Answer}\:\:{of} \\ $$$${question}:\left(\sqrt{\mathrm{2}}\:+\mathrm{1}\right)^{\mathrm{221}} =? \\ $$
Answered by a.lgnaoui last updated on 19/Feb/23
$$\left.\mathrm{2}\right)\mathrm{x}^{−\mathrm{17}} \\ $$