If X=3+2root2 then find the value of X-1/X whole to the power of 3
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x=3+2√2
=>1/x=1/(3+2√2)
=>1/x=(3-2√2)/(3²-(2√2)²)
=>1/x=(3-2√2)/(9-8)
=>1/x=3-2√2
So, x - 1/x = 3+2√2 - (3-2√2)=3+2√2 -3+2√2=4√2.
And, (x - 1/x)³=(4√2)³=64×2√2=128√2
=>1/x=1/(3+2√2)
=>1/x=(3-2√2)/(3²-(2√2)²)
=>1/x=(3-2√2)/(9-8)
=>1/x=3-2√2
So, x - 1/x = 3+2√2 - (3-2√2)=3+2√2 -3+2√2=4√2.
And, (x - 1/x)³=(4√2)³=64×2√2=128√2
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