Menu Close

Calcular-8-2-8-2-8-




Question Number 150029 by mathdanisur last updated on 08/Aug/21
Calcular:  (√(8 + 2(√(8 + 2(√(8 + ...)))))) = ?
$$\mathrm{Calcular}: \\ $$$$\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:…}}}\:=\:? \\ $$
Answered by nimnim last updated on 08/Aug/21
Let (√(8+2(√(8+2(√(8+......))))))=x  ⇒(√(8+2x))=x  ⇒x^2 −2x−8=0  ⇒(x−4)(x+2)=0  ⇒x=4 or x=−2(neglected)  ∴ x=4
$$\mathrm{Let}\:\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+……}}}=\mathrm{x} \\ $$$$\Rightarrow\sqrt{\mathrm{8}+\mathrm{2x}}=\mathrm{x} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{8}=\mathrm{0} \\ $$$$\Rightarrow\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{4}\:\mathrm{or}\:\mathrm{x}=−\mathrm{2}\left(\mathrm{neglected}\right) \\ $$$$\therefore\:\mathrm{x}=\mathrm{4} \\ $$
Commented by mathdanisur last updated on 08/Aug/21
Thankyou Ser
$$\mathrm{Thankyou}\:\boldsymbol{\mathrm{S}}\mathrm{er} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *