Question-155497

Question Number 155497 by VIDDD last updated on 01/Oct/21

Answered by amin96 last updated on 01/Oct/21

\sqrt{4 - \frac{1}{3 \sqrt{2}} \underset{⏟}{\sqrt{4 - \frac{1}{3 \sqrt{2}} \dots}}} = x

\sqrt{4 - \frac{1}{3 \sqrt{2}} x} = x \Rightarrow x^{2} = 4 - \frac{x}{3 \sqrt{2}} \Rightarrow 3 x^{2} \sqrt{2} + x - 12 \sqrt{2} = 0

Δ = 289 x = \frac{- 1 + 17}{6 \sqrt{2}} = \frac{8}{3 \sqrt{2}}

A = 10 + \log_{\frac{3}{2}} (\frac{1}{3 \sqrt{2}} \times \frac{8}{3 \sqrt{2}}) = 10 + \log_{\frac{3}{2}} \frac{4}{9} =

= 10 + 2 \log_{\frac{3}{2}} \frac{2}{3} = 10 + 2 \log_{\frac{3}{2}} {(\frac{3}{2})}^{- 1} = 10 - 2 = 8

Commented by puissant last updated on 01/Oct/21

N i c e S i r r e a l l y g r e a t \dots

Commented by VIDDD last updated on 01/Oct/21

g r e a t s i r, t h a n k s

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