a^2 −4a+2=0 a≻2 (√((a^4 +4)/(12a^2 )))=?


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Question Number 167488 by mathlove last updated on 18/Mar/22

$a^{2} - 4 a + 2 = 0 a ≻ 2$ $\sqrt{\frac{a^{4} + 4}{12 a^{2}}} = ?$
Commented by cortano1 last updated on 18/Mar/22
$(a−2)^2 =2 ⇒a=2+(√2) { ((a^2 =6+4(√2))),((a^4 =68+48(√2))) :} { ((a^4 +4=72+48(√2))),((12a^2 =72+48(√2))) :} (√((a^4 +4)/(12a^2 ))) = (√1) = 1$
${(a - 2)}^{2} = 2 \Rightarrow a = 2 + \sqrt{2}$ ${\begin{cases} a^{2} = 6 + 4 \sqrt{2} \\ a^{4} = 68 + 48 \sqrt{2} \end{cases}$ ${\begin{cases} a^{4} + 4 = 72 + 48 \sqrt{2} \\ {12 a}^{2} = 72 + 48 \sqrt{2} \end{cases}$ $\sqrt{\frac{a^{4} + 4}{{12 a}^{2}}} = \sqrt{1} = 1$
	Answered by mr W last updated on 18/Mar/22

	$a^{2} = 2 (2 a - 1) \Rightarrow 12 a^{2} = 24 (2 a - 1)$ $a^{4} = 4 (4 a^{2} - 4 a + 1) = 48 a - 28$ $a^{4} + 4 = 24 (2 a - 1)$ $\sqrt{\frac{a^{4} + 4}{12 a^{2}}} = 1$
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