\(\left\{{}\begin{matrix}r-s=4\\t-s=9\end{matrix}\right.\Rightarrow\left(t-s\right)-\left(r-s\right)=t-r=9-4=5\)

We have :

\(r^2+s^2+t^2-rs-st-rt\)

\(=\dfrac{2r^2+2s^2+2t^2-2rs-2st-2rt}{2}\)

\(=\dfrac{\left(r^2+s^2-2rs\right)+\left(r^2+t^2-2rt\right)+\left(t^2+s^2-2ts\right)}{2}\)

\(=\dfrac{\left(r-s\right)^2+\left(t-r\right)^2+\left(t-s\right)^2}{2}\)

\(=\dfrac{4^2+5^2+9^2}{2}=\dfrac{122}{2}=61\)

Ans : 61

{r−s=4t−s=9⇒(t−s)−(r−s)=t−r=9−4=5

We have :

r2+s2+t2−rs−st−rt

=2r2+2s2+2t2−2rs−2st−2rt2

=(r2+s2−2rs)+(r2+t2−2rt)+(t2+s2−2ts)2

=(r−s)2+(t−r)2+(t−s)22

=42+52+922=1222=61

Ans : 61