3-1-2-1-a-1-3-1-4-find-a-

Question Number 100302 by bemath last updated on 26/Jun/20

\sqrt{3^{- \frac{1}{2}} + 1} = \frac{\sqrt{a + 1}}{3^{- \frac{1}{4}}} . find a ?

Commented by bobhans last updated on 26/Jun/20

\frac{1}{\sqrt{3}} + 1 = \frac{a + 1}{3^{- \frac{1}{2}}} \Rightarrow \frac{\sqrt{3} + 1}{\sqrt{3}} = \sqrt{3} (a + 1)

\Rightarrow a + 1 = \frac{\sqrt{3} + 1}{3} = \frac{\sqrt{3}}{3} + \frac{1}{3}

a = \frac{\sqrt{3}}{3} - \frac{2}{3} = - \frac{2}{3} + 3^{- \frac{1}{2}}

Commented by Dwaipayan Shikari last updated on 26/Jun/20

3^{- \frac{1}{2}} + 1 = \frac{a + 1}{3^{- \frac{1}{2}}} \Rightarrow a + 1 = \frac{1}{3} + \frac{1}{\sqrt{3}} \Rightarrow a = \frac{1}{\sqrt{3}} - \frac{2}{3}