If x-1/x=3/2find the value of x square+1/x square
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Hi ,
x = 3 + 2√2 ---( 1 )
1/x = 1/( 3 + 2√2 )
= ( 3 - 2√2 )/[ ( 3 + 2√2 )( 3 - 2√2 )]
= ( 3 - 2√2 )/ [ 3² - ( 2√2 )² ]
= ( 3 - 2√2 ) / ( 9 - 8 )
= 3 - 2√2 ----( 2 )
x + 1/x = 3 + 2√2 + 3 - 2√2
= 6 ----( 3 )
Now ,
do the Square of equation ( 3 ) , we get
( x + 1/x )² = 6²
x² + 1/x² + 2 = 36
x² + 1/x² = 36 - 2
= 34
I hope this helps you.
: )
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