If x= 2+√3find the value of x^3+1/x^3
Answers
Answered by
3
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]
Answered by
0
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!!
thank you ⭐
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