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Question Number 79826 by Pratah last updated on 28/Jan/20

Commented by Pratah last updated on 28/Jan/20

please  solution.  help

$$\mathrm{please}\:\:\mathrm{solution}.\:\:\mathrm{help} \\ $$

Commented by mr W last updated on 28/Jan/20

you may repeat the question another  ∞ times, but you won′t get an other  answer than in Q78732...

$${you}\:{may}\:{repeat}\:{the}\:{question}\:{another} \\ $$$$\infty\:{times},\:{but}\:{you}\:{won}'{t}\:{get}\:{an}\:{other} \\ $$$${answer}\:{than}\:{in}\:{Q}\mathrm{78732}... \\ $$

Commented by Pratah last updated on 28/Jan/20

solution pls

$$\mathrm{solution}\:\mathrm{pls} \\ $$

Commented by mr W last updated on 28/Jan/20

f(x)=6−3^(x/(√(x^2 +2x+6)))   ⇒f(f(f(x)))=x  ⇒f(x)=x  ⇒x≈3.8001349 (only numerically)

$${f}\left({x}\right)=\mathrm{6}−\mathrm{3}^{\frac{{x}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{6}}}} \\ $$$$\Rightarrow{f}\left({f}\left({f}\left({x}\right)\right)\right)={x} \\ $$$$\Rightarrow{f}\left({x}\right)={x} \\ $$$$\Rightarrow{x}\approx\mathrm{3}.\mathrm{8001349}\:\left({only}\:{numerically}\right) \\ $$

Commented by Pratah last updated on 28/Jan/20

step by step solution sir pls

$$\mathrm{step}\:\mathrm{by}\:\mathrm{step}\:\mathrm{solution}\:\mathrm{sir}\:\mathrm{pls} \\ $$

Commented by mr W last updated on 28/Jan/20

there is no “nice” solution possible.  due to symmetry x=y=z  all the equations are the same  (√(x^2 +2x+6)) log_3  (6−x)=x  but you can solve it only numerically:  x≈3.800135

$${there}\:{is}\:{no}\:``{nice}''\:{solution}\:{possible}. \\ $$$${due}\:{to}\:{symmetry}\:{x}={y}={z} \\ $$$${all}\:{the}\:{equations}\:{are}\:{the}\:{same} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{6}}\:\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{6}−{x}\right)={x} \\ $$$${but}\:{you}\:{can}\:{solve}\:{it}\:{only}\:{numerically}: \\ $$$${x}\approx\mathrm{3}.\mathrm{800135} \\ $$

Commented by Pratah last updated on 28/Jan/20

ok

$$\mathrm{ok} \\ $$

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