Question : If $(a+b+c)=14$ and $\left(a^3+b^3+c^3-3abc\right)=98$, find the value of $\left(a^2+b^2+c^2\right)$.

Question : If $(a+b+c)=19$ and $\left(a^2+b^2+c^2\right)=155$, find the value of $(a-b)^2+(b-c)^2+(c-a)^2$

Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Question : If $\left (a+\frac{1}{b} \right)=1$ and $\left (b+\frac{1}{c} \right)=1$, the value of $\left (c+\frac{1}{a} \right)$ is:

Question : If $a^{2}=b+c,b^{2}=c+a,c^{2}=a+b$, the value of $3\left (\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\right)$ is: