Question

If ab= 2a+3b then minimum value of ab is

Answer 1

hey dear

the minimum value of ab is 5
hope it helps uu

Answer 2

The minimum value of $ab$ is $24$

Step-by-step explanation:

Given,

If $ab= 2a+3b$ then minimum value of $ab$ ..?

$ab= 2a+3b$__1

Using $AM\geq GM$,

 $\frac{2a+3b}{2} \geq (6ab)^{\frac{1}{2} }ab$

⇒$(2a+3b)\geq 2(6ab)^{\frac{1}{2} }$

From equation-1,

⇒$ab\geq 2(6ab)^{\frac{1}{2} }$

⇒$(ab)^{\frac{1}{2} }\geq 2(6)^{\frac{1}{2} }$

⇒$(ab)^{\frac{1}{2} }\geq (24)^{\frac{1}{2} }$

⇒$ab\geq 24$

∴ From above expression the minimum value of $ab$ is $24$