If a =2 +under root 3 ,find the value of a power 3 - 1 by a power 3

1.	If a =2 +under root 3 ,find the value of a power 3 - 1 by a power 3
Answer» Step-by-step EXPLANATION: a =2+√3 1/a = 1/2+√3 = (2-√3)/(2+√3)(2-√3) = (2-√3)/(4-3) = (2-√3) a+ 1/a = 4 SQUARING on both sides we get ${(a + \frac{1}{a})}^{2} = 16 = > {a}^{2} + \frac{1}{{a}^{2}} + 2 = 16$ $= > {a}^{2} + \frac{1}{ {a}^{2}} = 14$ a -1/a =>(2+√3)-(2-√3) =>2√3. ${a}^{3} - \frac{1}{{a}^3} = (a - \frac{1}{a})({a}^{2} + \frac{1}{ {a}^{2}} + 1) = >$ ${a}^{3} - \frac{1}{ {a}^{3}} = 2 \sqrt{3}(14 + 1) = 30 \sqrt{3}$ Hope it helps you.

Answer»

Step-by-step EXPLANATION:

a =2+√3

1/a = 1/2+√3 = (2-√3)/(2+√3)(2-√3) =

(2-√3)/(4-3) = (2-√3)

a+ 1/a = 4 SQUARING on both sides we get

${(a + \frac{1}{a})}^{2} = 16 = > {a}^{2} + \frac{1}{{a}^{2}} + 2 = 16$