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I: The real number x when added to its inverse gives the minim

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I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1
II: If product of the two positive numbers is 400, then the minimum value of their sum is 20
which of the above statements are true

only I is true

only II is true

both I and II are true

niether I nor II are true

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I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1
II: If product of the two positive numbers is 400, then the minimum value of their sum is 20
which of the above statements are true

12 mins ago

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Text solutionVerified

(I)

x + \frac{1}{x} = f (x)

Use AM & GM

\frac{x + \frac{1}{x}}{2} \geq (1)^{\frac{1}{2}}

x + \frac{1}{x} \geq 2

(II)

x y = 400

f (x) = x + \frac{400}{x}

Use AM & GM

\frac{x + \frac{400}{x}}{2} \geq (400)^{\frac{1}{2}}

x + \frac{400}{x} \geq 40

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Question Text	I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1 II: If product of the two positive numbers is 400, then the minimum value of their sum is 20 which of the above statements are true
Answer Type	Text solution:1
Upvotes	150

I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1II: If product of the two positive numbers is 400, then the minimum value of their sum is 20which of the above statements are true

Text solutionVerified

Practice questions from similar books

I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1
II: If product of the two positive numbers is 400, then the minimum value of their sum is 20
which of the above statements are true