Này thì khó :))Ta có công thức:Cn−kn=CknNên $VT=C^1_x+C^2_x+C^3_x+...+C^{10}_x (*)$Ta xét khai triển: $(1+1)^x=C^0_x+C^1_x+C^2_x+...+C^{10}_x=2^x\Rightarrow (*)=2^x-C^0_x$ĐK: $n\in N^*$Pt $\Leftrightarrow C^1_x+C^2_x+C^3_x+...+C^{10}_x=1023$$\Leftrightarrow 2^x-C^0_x=1023$$\Leftrightarrow 2^x=1024$$\Leftrightarrow 2^x=2^{10}$$\Leftrightarrow x=10$
Pt $\Leftrightarrow C^1_x+C^2_x+C^3_x+...+C^{10}_x=1023$$\Leftrightarrow C^0_x+C^1_x+C^2_x+...+C^{10}_x=1024$$<=>C^0_x+C^1_x+C^2_x+...+C^{10}_x=2^{10}$mà $C^0_x+C^1_x+...+C^x_x=2^x$$=>x=10$