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Question-199801




Question Number 199801 by Calculusboy last updated on 09/Nov/23
Answered by Frix last updated on 09/Nov/23
x=a(√(b−a(√(b−a(√(b−...))))))  x=a(√(b−x))  x^2 =a^2 (b−x)  x^2 +a^2 x−a^2 b=0  x=−(a^2 /2)+((a^2 (√(a^2 +4b)))/2)  a=((√2)/6)∧b=4  x=(4/9)  6+((ln (4/9))/(ln (3/2)))=6−2=4
$${x}={a}\sqrt{{b}−{a}\sqrt{{b}−{a}\sqrt{{b}−…}}} \\ $$$${x}={a}\sqrt{{b}−{x}} \\ $$$${x}^{\mathrm{2}} ={a}^{\mathrm{2}} \left({b}−{x}\right) \\ $$$${x}^{\mathrm{2}} +{a}^{\mathrm{2}} {x}−{a}^{\mathrm{2}} {b}=\mathrm{0} \\ $$$${x}=−\frac{{a}^{\mathrm{2}} }{\mathrm{2}}+\frac{{a}^{\mathrm{2}} \sqrt{{a}^{\mathrm{2}} +\mathrm{4}{b}}}{\mathrm{2}} \\ $$$${a}=\frac{\sqrt{\mathrm{2}}}{\mathrm{6}}\wedge{b}=\mathrm{4} \\ $$$${x}=\frac{\mathrm{4}}{\mathrm{9}} \\ $$$$\mathrm{6}+\frac{\mathrm{ln}\:\frac{\mathrm{4}}{\mathrm{9}}}{\mathrm{ln}\:\frac{\mathrm{3}}{\mathrm{2}}}=\mathrm{6}−\mathrm{2}=\mathrm{4} \\ $$
Commented by Calculusboy last updated on 10/Nov/23
thanks
$$\boldsymbol{{thanks}} \\ $$

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