ข้อสอบคณิต 9 สามัญ - ปี 2559

$$\begin{gathered} \mathrm{จากโจทย์} 9^{\mathrm{logx}}-10\left(3^{\mathrm{logx}}\right)+9 =0 \\ \mathrm{จะได้} 3^{2\mathrm{logx}}-10\left(3^{\mathrm{logx}}\right)+9 =0 \\ {\left(3^{\mathrm{logx}}\right)}^2-10\left(3^{\mathrm{logx}}\right)+9=0 \\ \mathrm{กำหนดให้}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{3}^{\log x}=A \\ \mathrm{จะได้}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{A}^2-10A+9=0 \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(A-1)(A-9)=0 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{A}-1=0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{หรือ}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{A}-9=0 \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}{3}^{\mathrm{logx}}-1=0 \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{3}^{\mathrm{logx}}-9=0 \\ 3^{\mathrm{logx}}=1 3^{\mathrm{logx}}=9 \\ 3^{\mathrm{logx}}=3^0 3^{\mathrm{logx}}=3^2 \\ \mathrm{logx}=0 \mathrm{logx}=2 \\ \mathrm{x}={10}^0 \mathrm{x}={10}^2 \\ \mathrm{x}=1 \mathrm{x}=100 \\ \mathrm{ดังนั้น} \mathrm{ผลบวกคำตอบ} \mathrm{คือ} 1+100=101 \end{gathered}$$