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Question Number 109428 by mathdave last updated on 23/Aug/20

Commented by som(math1967) last updated on 23/Aug/20

$$\mathrm{is}\mathrm{it}2.5?$$

Commented by mathdave last updated on 23/Aug/20

$$yes$$

Answered by Dwaipayan Shikari last updated on 23/Aug/20

$$4{\left(\frac{\sqrt{5}-1}{4}\right)}^2+\frac{\sqrt{5}-1}{2}+2=\frac{6-2\sqrt{5}}{4}+\frac{\sqrt{5}-1}{2}+2=1+2=3$$

Answered by som(math1967) last updated on 23/Aug/20

$$4\times \frac{{(\sqrt{5}-1)}^2}{16}+2\times \frac{\sqrt{5}-1}{4}+2.5★$$$$=\frac{5+1-2\sqrt{5}}{4}+\frac{\sqrt{5}-1}{2}+2.5$$$$=\frac{6-2\sqrt{5}+2\sqrt{5}-2}{4}+2.5$$$$=\frac{4}{4}+2.5=3.5$$$$\mathrm{ans}\left(\mathrm{b}\right)$$$$★\sin 18=\frac{\sqrt{5}-1}{4}$$

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