if x+1/x=5+√2,find the value of x^3 +1/x^3
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Given, x−x1=5
Squaring both the sides,
⇒(x−x1)2=52
⇒x2+x21−2(x)(x1)=25
⇒x2+x21=25+2
⇒x2+x21=27
Now,
x3−x31
=(x−x1)[(x)2+(x1)2+(x)(x1)]
=5(27+1)
=140
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