If x+1/x=5+√2, find the value of x^3 +1/x^3
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Answer:
x+1/x=5+√2
x^3+1/x^3
=(x+1/x)^3-3.x.1/x(x+1/x)
=(5+√2)^3-3(5+√2)
=(5+√2){(5+√2)^2-3}
=(5+√2)(25+2+2.5.√2-3)
=(5+√2)(24+10√2)
=120+24√2+50√2+20
=140+74√2
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