if 3-2√2 find x²+1/x²
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Answer :
x² + 1/x² = 34
Solution :
- Given : x = 3 - 2√2
- To find : x² + 1/x²
We have ;
x = 3 - 2√2
Then ,
1/x = 1/(3 - 2√2)
Now ,
Rationalising the denominator of the term in RHS , we have ;
=> 1/x = (3 + 2√2) / (3 - 2√2)(3 + 2√2)
=> 1/x = (3 + 2√2) / [ 3² - (2√2)² ]
=> 1/x = (3 + 2√2) / (9 - 8)
=> 1/x = (3 + 2√2) / 1
=> 1/x = 3 + 2√2
Now ,
We know that ,
(a + b)² = a² + b² + 2ab
Thus ,
=> (x + 1/x)² = x² + (1/x)² + 2•x•(1/x)
=> (3 - 2√2 + 3 + 2√2)² = x² + 1/x² + 2
=> 6² = x² + 1/x² + 2
=> 36 = x² + 1/x² + 2
=> x² + 1/x² = 36 - 2
=> x² + 1/x² = 34
Hence , x² + 1/x² = 34 .
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