Comment-resoudre-cette-eqution-2-x-3-y-2-1-

Question Number 53063 by Tristan last updated on 16/Jan/19

Comment resoudre cette eqution

2^{x} \times 3 - y^{2} = - 1

Answered by MJS last updated on 18/Jan/19

(1)

y = \pm \sqrt{3 \times 2^{x} + 1}

\Rightarrow x \in R

(2)

2^{x} = \frac{y^{2} - 1}{3}

x \ln 2 = \ln (y^{2} - 1) - \ln 3

x = \log_{2} (y^{2} - 1) - \log_{2} 3

\Rightarrow y^{2} > 1 \Rightarrow y \in R ∖ [- 1; 1]

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