Class 9 Exam > Class 9 Questions > If x = 2+root 3 find x3 + 1/x3?
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If x = 2+root 3 find x3 + 1/x3
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If x = 2+root 3 find x3 + 1/x3?
Given:
x = 2 + √3
To Find:
x^3 + 1/x^3
Solution:
Step 1: Finding x^3
x^3 = (2 + √3)^3
Expanding using the formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
x^3 = 2^3 + 3*(2^2)*(√3) + 3*2*(√3)^2 + (√3)^3
x^3 = 8 + 12√3 + 18 + 3√3
x^3 = 26 + 15√3
Step 2: Finding 1/x^3
1/x^3 = 1/(26 + 15√3)
Multiplying numerator and denominator by the conjugate of the denominator to rationalize the denominator
1/x^3 = (26 - 15√3)/(26^2 - (15√3)^2)
1/x^3 = (26 - 15√3)/(676 - 675)
1/x^3 = (26 - 15√3)/1
1/x^3 = 26 - 15√3
Step 3: Final Calculation
x^3 + 1/x^3 = 26 + 15√3 + 26 - 15√3
x^3 + 1/x^3 = 52
Therefore, x^3 + 1/x^3 = 52
x = 2 + √3
To Find:
x^3 + 1/x^3
Solution:
Step 1: Finding x^3
x^3 = (2 + √3)^3
Expanding using the formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
x^3 = 2^3 + 3*(2^2)*(√3) + 3*2*(√3)^2 + (√3)^3
x^3 = 8 + 12√3 + 18 + 3√3
x^3 = 26 + 15√3
Step 2: Finding 1/x^3
1/x^3 = 1/(26 + 15√3)
Multiplying numerator and denominator by the conjugate of the denominator to rationalize the denominator
1/x^3 = (26 - 15√3)/(26^2 - (15√3)^2)
1/x^3 = (26 - 15√3)/(676 - 675)
1/x^3 = (26 - 15√3)/1
1/x^3 = 26 - 15√3
Step 3: Final Calculation
x^3 + 1/x^3 = 26 + 15√3 + 26 - 15√3
x^3 + 1/x^3 = 52
Therefore, x^3 + 1/x^3 = 52
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If x = 2+root 3 find x3 + 1/x3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x = 2+root 3 find x3 + 1/x3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2+root 3 find x3 + 1/x3?.
If x = 2+root 3 find x3 + 1/x3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x = 2+root 3 find x3 + 1/x3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2+root 3 find x3 + 1/x3?.
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