Question

tìm x\(\in\)N để A=\(\dfrac{5x-2}{2x+1}\) có GTLN .Tìm GTLN đó.

Answer 1

A= \(\dfrac{5x-2}{2x+1}=\dfrac{\left(2x+1\right)+3x-3}{2x+1}=1+\dfrac{3x-3}{2x+1}\)

A=\(1+\dfrac{\left(2x+1\right)+x-4}{2x+1}=1+1\dfrac{x-4}{2x+1}\)

A= \(2+\dfrac{x-4}{2x+1}=2+\dfrac{2.\left(x-4\right)}{2.\left(2x+1\right)}=2+\dfrac{2x-8}{2\left(2x+1\right)}\)

A= \(2+\dfrac{1}{2}.\left(\dfrac{2x-8}{2x+1}\right)=2+\dfrac{1}{2}.\left(1-\dfrac{9}{2x+1}\right)\)

A=2+\(\dfrac{1}{2}-\dfrac{9}{4x+2}\)

Để Amax => \(\left(2+\dfrac{1}{2}-\dfrac{9}{4x+2}\right)max\) => \(\left(\dfrac{9}{4x+2}\right)min\)=> (4x+2)max và 4x+2 \(\in\)N => Không có giá trị nào để Amax\(\)

Tick cho tớ nha ><