Question

if x is equal to 2+root 3 then find 1 upon x cube + x cube​

Answer 1

Solution:

It is given that,

i)x = 2+√3 ---(1)

ii)1/x =1/(2+√3)

= (2-√3)/[(2+√3)(2-√3)]

= (2-√3)/[2² - (√3)²]

= (2-√3)/(4-3)

= 2-√3 ----(2)

iii ) x + 1/x

= 2+√3+2-√3

= 4 ----(3)

Now ,

x³+1/x³

= (x+1/x)³ -3(x+1/x)

= 4³ - 3×4

= 64 - 12

= 52

Therefore,

x³+1/x³ = 52

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