Suppose `a ,b ,c` are the roots of the cubic `x^3-x^2-2=0.` Then the value of `a^3+b^3+c^3` is _____.

Answer

7

Explanation

Given `a+b+c=1" "(1)`
`ab+bc+ca=0" "(2)`
`abc=2" "(2)`
Now `(a+b+c)^(2)=1" "(3)`
`a^(2)+b^(2)+c^(2)+2sumab=1`
`:.a^(2)+b^(2)+c^(3)=1`
Now, `a^(3)+b^(3)+c^(3)-3ab=(a+b+c)[suma^(2)-sumab]`
`=1(1-0)=1`
`:.a^(3)+b^(3)+c^(3)=1+3abc=1+3xx2=7`