Principal-Agent Problem with Two Agents
While it's not explicitly mentioned in the question, it seems safe to assume that the manager gets to observe separately the outcome of each worker, i.e. the value of $v_i$ for $i=1,2$. If this is the case, the IR and IC conditions depend on the exact terms of the contract.
For example, suppose the manager conditions each worker $i$'s wage on both $v_i$ and $v_{-i}$. That is,
\begin{equation}
w_i(v_i,v_{-i})=
\begin{cases}
w^{11}&amp;\text{if $v_i=10,v_{-i}=10$}\\
w^{10}&amp;\text{if $v_i=10,v_{-i}=0$}\\
w^{01}&amp;\text{if $v_i=0,v_{-i}=10$}\\
w^{00}&amp;\text{if $v_i=0,v_{-i}=0$}
\end{cases}
\end{equation}
Further, let $p_h^{11}$ denote the probability that both workers produce the high-value outcome (indicated by the superscript $11$) when $i$ works hard (indicated by subscript $h$) and the fellow worker $-i$ also works hard (we suppress the second $h$ in the subscript as we always assume that $-i$ works hard). In more compact notations,
\begin{equation}
p_h^{11}=\Pr(v_i=10,v_{-i}=10 \mid a_i=a_h, a_{-i}=a_h).
\end{equation}
Probabilities $p_h^{10},p_h^{01},p_h^{00},p_l^{11},p_l^{10},p_l^{01},p_l^{00}$ are similarly defined.
Then, the IR constraint for worker $i$, assuming worker $-i$ is going to work hard, would be
\begin{equation}
p_h^{11}\sqrt{w^{11}}+p_h^{10}\sqrt{w^{10}}+p_h^{01}\sqrt{w^{01}}+p_h^{00}\sqrt{w^{00}}-a_h\ge 1.
\end{equation}
The IC constraint for worker $i$, again assuming worker $-i$ is going to work hard, would be
\begin{multline}
p_h^{11}\sqrt{w^{11}}+p_h^{10}\sqrt{w^{10}}+p_h^{01}\sqrt{w^{01}}+p_h^{00}\sqrt{w^{00}}-a_h\\ \ge p_l^{11}\sqrt{w^{11}}+p_l^{10}\sqrt{w^{10}}+p_l^{01}\sqrt{w^{01}}+p_l^{00}\sqrt{w^{00}}-a_l.\end{multline}
From the information given by the problem, you should be able to figure out the eight probabilities.
If the wage is conditioned simply on $v_i$, or
\begin{equation}
w_i(v_i)=
\begin{cases}
w^1&amp;\text{if $v_i=10$}\\
w^0&amp;\text{if $v_i=0$}
\end{cases}
\end{equation}
then the IR and IC for each worker would be
\begin{align}
0.7\sqrt{w^1}+0.3\sqrt{w^0}-a_h&amp;\ge 1 \tag{IR}\\
0.7\sqrt{w^1}+0.3\sqrt{w^0}-a_h&amp;\ge 0.3\sqrt{w^1}+0.7\sqrt{w^0}-a_l. \tag{IC}
\end{align}