Question

2^x+2^(-x)=2cos²((x²+x)/3)
find x​

Answer 1

Answer:

$2 {cos}^{2} ( \frac{ {x}^{2 \times} + x }{6} )= {2}^{x} +2 { - }^{x} \\ ∵ {2}^{n} +2 { - }^{x} ≥2 \sqrt{ {2}^{x} } .2 { - }^{x} =2 \\ </p><p></p><p>So, by AM−GM, \\ 2 {cos}^{2} ( \frac{ {x}^{2} + x }{6} )≥2 \\ ⇒ {cos}^{2} ( \frac{ {x}^{2} + x}{6} )≥1 \\ ∵cos0=1 \\ ⇒ \frac{ {x}^{2} + x }{6} = 0 \\ ⇒x(x+1)=0 \\ </p><p></p><p>⇒x=0 \\ −1  \: is \: \: your\: \:answer$

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