已知实数x、y满足x2-2x+4y=5，则x+2y的最大值为．

Question

已知实数x、y满足x²-2x+4y=5，则x+2y的最大值为______．

Answer 1

∵实数x、y满足x²-2x+4y=5
∴y=(5−x2+2x)/(4)
∴x+2y=x+2×(5−x2+2x)/(4)=-(1)/(2)x²+2x+(5)/(2)
∴最大值为(4×(−(1)/(2)) ×(5)/(2)−22)/(4× (−(1)/(2)))=(9)/(2)．