If every pair from among the equations $x^2+ax+bc=0$, $x^2+bx+ca=0$ and $x^2+cx+ab=0$ has a common root, then

If $f\left(x\right)$ is a polynomial of degree $4$ with rational coefficients and touches $x$-axis at $\left(\sqrt{2}, 0\right)$, then for the equation $f\left(x\right)=0$,

The real $x$ satisfying the equation $x^3+\frac{1}{x^3}+x^2+\frac{1}{x^2}-6\left(x+\frac{1}{x}\right)-7=0$ is$/$are