Question 90 of 157MediumMCQ
If x is real, the maximum value of \[{{3{x^2} + 9x + 17} \over {3{x^2} + 9x + 7}}\] is Solutions · 1
Official solution
\[y = {{3{x^2} + 9x + 17} \over {3{x^2} + 9x + 7}}\]
\[3{x^2}\left( {y - 1} \right) + 9x\left( {y - 1} \right) + 7y - 17 = 0\]
\[D \ge 0\] as x is real
\[81{\left( {y - 1} \right)^2} - 4 \times 3\left( {y - 1} \right)\left( {7y - 17} \right) \ge 0\]
\[ \Rightarrow \left( {y - 1} \right)\left( {y - 41} \right) \le 0\]
\[ \Rightarrow 1 \le y \le 41\]
\[\therefore\] Max value of y is 41 Answer the question to unlock