For ensuring dissipation of same energy in all three resistors (R1, R…

As voltage across the resistors $R_2$ and $R_3$ is same and they show same dissipation of energy, so using the relation for energy, $H=\frac{V^2}{R} t$, we get $R_2=R_3$

Thus, the current in each resistor $R_2$ and $R_3$ will be $\frac{I}{2}$.

i.e., $I_1=\frac{I}{2}$ and $I_2=\frac{I}{2}$

Since the energy dissipation is same in all the three resistors, so

$I^2 R_1 t=I_1^2 R_2 t$

or  $I^2 R_1 t=\left(\frac{I}{2}\right)^2 R_2 t$

or  $R_1=\frac{R_2}{4}$