EBTANAS 1998 6 ---------------------------- [tex] \sqrt{5+\sqrt{3} } [/tex] Mohon penjelasannya, mudah-mudahan pertanyaan ini segera dijawab

[tex] \sqrt{5 + \sqrt{3} } = \sqrt{a} + \sqrt{b} \\5 + \sqrt{3} = {( \sqrt{a} + \sqrt{b})}^{2} \\ 5 + \sqrt{3} = (a + b) + 2 \sqrt{ab} \\ a + b = 5 \: \: \: \: \: b = 5 - a \\ 2 \sqrt{ab} = \sqrt{3} \: \: \: \: \: \sqrt{ab} = \frac{ \sqrt{3} }{2} \: \: \: \: \: ab = \frac{3}{4} \: \: \: \: \: a(5 - a) = \frac{3}{4} \\ 5a - {a}^{2} = \frac{3}{4} \: \: \: \: \: \: 20a - 4 {a}^{2} = 3 \: \: \: \: \: \: 4 {a}^{2} - 20a + 3 = 0 \\ {(2a - 5)}^{2} - 25 + 3 = 0 \: \: \: \: \: \: {(2a - 5)}^{2} = 22 \\ 2a - 5 = \sqrt{22} \: \: \: \: \: a = \frac{5 + \sqrt{22} }{2} \: \: \: \: \: \: \: b = \frac{5 - \sqrt{22} }{2} [/tex]