if X = 3+2√2 , find the value of X ^ 2 + 1/x^2
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Solution
Given :-
- x = 3 + 2√2
Find :-
- Value of x² + 1/x²
Explanation
First Calculate 1/x
➡ 1/x = 1/(3+2√2)
Rationalize denominator
➡1/x = (3-2√2)/(3-2√2)(3+2√2)
➡1/x = (3-2√2)/(9-8)
➡1/x = (3-2√2)
Squaring both side,
➡ 1/x² = (3-2√2)²
➡1 )/x² = [3² + (2√2)² - 2×3×(2√2)]
➡1/x² = 9 + 8 - 12√2
➡1/x² = 17 - 12√2
Now, calculate,
➡ x² + 1/x² = (3+2√2) + (17 - 12√2)
➡x² + 1 /x² = 20 - 10√2
Hence
- Value of x² + 1 /x² be = 10(2 - √2)
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Answered by
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Step-by-step explanation:
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