Question

If a=2+ root 3 then a cube + 1/a cube equqls to

Answer 1

Answer:

52

Step-by-step explanation:

by the given data:

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

$a=2+\sqrt{3}$    and     $\frac{1}{a} = \frac{1}{2+\sqrt{3} } =\frac{1(2-\sqrt{3} ) }{(2+\sqrt{3})(2-\sqrt{3}) }$

                                                $= 2-\sqrt{3}$

The above result was obtained by rationalizing

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

By above data

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

           $= (4)^3 -3(4)$

           =64-12= 52