Question 120

If x and y are positive real numbers and xy = 8, then the minimum value of 2x + y is

Solution

As $$x$$ & $$y$$ are positive real numbers, we can use AM $$\geq$$ GM

Let two numbers be $$2x$$ and $$y$$

=> $$\frac{2x + y}{2} \geq \sqrt{2xy}$$

=> $$2x + y \geq 2\sqrt{16}$$

=> $$2x + y \geq 8$$

=> Minimum value of $$(2x + y)$$ is 8

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