Question

If x= 2+√3find the value of x^3+1/x^3

Answer 1

x = 2+√3

x^3 = (2+√3)^3

= 2^3 + √3^3 + 3•2•√3(2+√3)

= 8 + 3√3 + 6√3(2 + √3)

= 8 + 3√3 + 12√3 + 18

= 26 + 3√3 + 12√3

= 26 + √3(3 + 12)

= 26 + 15√3 ...eq.01

x^3 = 26 + 15√3

1/x^3 = 1/(26 + 15√3)

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

= (26 - 15√3)/[26^2 - {15^2 × 3}]

= (26 - 15√3)/{676 - 675}

= 26 - 5√3 ...eq.02

x^3 + 1/x^3

= 26 + 15√3 + 26 - 15√3

= 52 [ANS]

Answer 2

Step-by-step explanation:

x = 2+√3

x^3 = (2+√3)^3

= 2^3 + √3^3 + 3•2•√3(2+√3)

= 8 + 3√3 + 6√3(2 + √3)

= 8 + 3√3 + 12√3 + 18

= 26 + 3√3 + 12√3

= 26 + √3(3 + 12)

= 26 + 15√3 ...eq.01

x^3 = 26 + 15√3

1/x^3 = 1/(26 + 15√3)

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

= (26 - 15√3)/[26^2 - {15^2 × 3}]

= (26 - 15√3)/{676 - 675}

= 26 - 5√3 ...eq.02

x^3 + 1/x^3

= 26 + 15√3 + 26 - 15√3

= 52 [ANS]

hope this helps you!!

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