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Question Number 186271 by cherokeesay last updated on 02/Feb/23

Answered by HeferH last updated on 02/Feb/23

Commented by HeferH last updated on 02/Feb/23

$$x+\frac{x}{\sqrt{3}}+\frac{2}{\sqrt{3}}(x+x\sqrt{3})=6$$$$3x+3x\sqrt{3}=6\sqrt{3}$$$$x(3+3\sqrt{3})=6\sqrt{3}$$$$x=\frac{2\sqrt{3}}{1+\sqrt{3}}=\frac{6-2\sqrt{3}}{2}=3-\sqrt{3}$$$$x^2={(3-\sqrt{3})}^2=12-6\sqrt{3}\approx 1.6u^2$$$$$$

Commented by cherokeesay last updated on 02/Feb/23

$$Nice!thankyou$$

Answered by mr W last updated on 02/Feb/23

Commented by mr W last updated on 02/Feb/23

$$\frac{2R}{\sqrt{3}}+\frac{R}{\sqrt{3}}=6$$$$\Rightarrow R=2\sqrt{3}$$$$a+\sqrt{3}a=R=2\sqrt{3}$$$$\Rightarrow a=\frac{2\sqrt{3}}{1+\sqrt{3}}=\sqrt{3}(\sqrt{3}-1)=3-\sqrt{3}$$$$a^2={(3-\sqrt{3})}^2=6(2-\sqrt{3})\approx 1.608$$

Commented by cherokeesay last updated on 02/Feb/23

$$great!thankyou$$

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