An algebra problem by Raushan Sharma

Algebra Level 2

What is the minimum value of 2 x + 1 x 2\sqrt{x} + \frac{1}{x} given that x > 0 x > 0


The answer is 3.00.

Raushan Sharma by Raushan Sharma , 20, India

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1 solution

Rishabh Jain
Mar 6, 2016

S = 2 x + 1 x = x + x + 1 x \large \mathfrak{S}=2\sqrt x+\dfrac 1x=\sqrt x +\sqrt x +\dfrac 1x

Applying AM ≥ \geq GM

S ≥ 3 x × x × 1 x 3 = 3 \large \mathfrak S\geq 3\sqrt[3]{\sqrt{x}\times\sqrt{x}\times\dfrac{1}{x}} =\boxed{\Large 3}

Equality occurs when x = 1 x=1 .

5 Helpful 0 Interesting 0 Brilliant 0 Confused

It should be S ≥ 3 x × x × 1 x 3 \mathfrak{S}\geq 3\sqrt[3]{\sqrt{x}\times\sqrt{x}\times\dfrac{1}{x}}

Abdur Rehman Zahid - 5 years, 3 months ago

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Typo.....Thanks!!

Rishabh Jain - 5 years, 3 months ago

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