Question

if x is equals to 2 + under root 3 find the value of x cube + 1 by x cube

Answer 1

HELLO DEAR,


given that:-

x = (2 + √3)


on cubing both side,

we get,

x³ = [8 + 3√3 + 6√3(2 + √3)]

x³ = (8 + 3√3 + 12√3 + 18)

x³ = (26 + 15√3)---------(1)

now,

1/x³ = 1/(26 + 15√3) × (26 - 15√3)/(26 - 15√3)

1/x³ = (26 - 15√3)/(676 - 675)

1/x³ = (26 - 15√3)----------(2)


NOW,

adding-----(1) & ------(2)


we get,

(x³ + 1/x³) = (26 + 15√3) + (26 - 15√3)

(x³ + 1/x³) = (26 + 26) + (15√3 - 15√3)

(x³ + 1/x³) = 52



I HOPE ITS HELP YOU DEAR,
THANKS