22. Given that $169(157-77 x)^{2}+100(201-100 x)^{2}=26(77 x-157)(1000 x-2010)$, find the value of $x$.
22. Ans: 31 .
Let $a=1001 x-2041$ and $b=1000 x-2010$.
Then the equation becomes $a^{2}+b^{2}=2 a b$. Thus $(a-b)^{2}=0$. The result follows.