Question

a cube + 1 / a cubewhere a =2+√3

Answer 1

a cube+1/a cube can be written as (a+1/a)(a square + 1/a square +1) a=2+√3 so 1/a is 2-√3 so a+1/a is 4 , a square +1/a square +1 = (a+1/a) square -1 so answer is 60 since 4(15)

Answer 2

a^3+1/a^3
Put the valu of a=2+√3
=(2+√3)^3+1/(2+√3)^3
=8+3√3+3×2×√3(2+√3)+1/8+3√3+3×2×√3(2+√3)
=8+3√3+6√3(2+√3)+1/8+3√3+6√3(2+√3)
=8+3√3+12√3+18+1/8+3√3+12√3+18
=26+15√3+1/26+15√3
$26 + 15 \sqrt{3} + \frac{1}{26 + 15 \sqrt{3} }$
$\frac{(26 + 15 \sqrt{3} )(26 + 15 \sqrt{3} ) + 1}{26 + 15 \sqrt{3} }$
$\frac{(676 + 675 + 2 \times 26 \times 15 \sqrt{3} ) + 1}{26 + 15 \sqrt{3} }$
$\frac{(1351 + 780 \sqrt{3} )+ 1 }{26 + 15 \sqrt{3} }$
=1352+780√3/26+15√3

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