Question

IF a= 2+√3
Find the value
a (power 3) +1/a (power 3)

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Answer 1

Hęřę įš ùř ąńšwęř....♥♡♥

$\frac{1}{a} = \frac{1}{2 + \sqrt{3} }$

$= \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$= \frac{2 - \sqrt{3} }{(2) {}^{2} - (\sqrt{3}) {}^{2} }$

$= \frac{2 - \sqrt{3} }{4 - 3}$

$= 2 - \sqrt{3}$

Hence,

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

$= > (2 + \sqrt{3} + 2 - \sqrt{3} )$

$= > 4$

Hence,

$(a + \frac{1}{a} ) = 4$

cubing both the sides....

${(a + \frac{1}{a} )}^{3} = (4) {}^{3}$

$a {}^{3} + \frac{1}{a {}^{3} } + 3a \frac{1}{a} (a + \frac{1}{a}) = 4$

$= > a {}^{3} + \frac{1}{ {a}^{3} } + 3(4) = 64$

$= > a {}^{3} + \frac{1}{ {a}^{3} } = 52$

Hope it helps uh mate....

Answer 2

Answer:

Step-by-step explanation:

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