If x > 0, then the minimum value of x1000+x900+x90+x6+x1996 is

x1000+x900+x90+x6+x1996 splitting x1996 into x1 1996 times and adding we get as AM≥GM2000x1000+x900+x90+x6+x1+....+x1≥1Hence x1000+x900+x900+x6+x1996≥2000

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If x > 0, then the minimum value of x^{1000}+x^{900}+x^{90}+x

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If x > 0, then the minimum value of $x^{1000} + x^{900} + x^{90} + x^{6} + \frac{1996}{x}$ is

1000

2000

1996

3000

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If x > 0, then the minimum value of

x^{1000} + x^{900} + x^{90} + x^{6} + \frac{1996}{x}

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Text solutionVerified

x^{1000} + x^{900} + x^{90} + x^{6} + \frac{1996}{x}

splitting

\frac{1996}{x}

into

\frac{1}{x}

1996 times and adding we get

as AM

\geq

\frac{x ^{1000} + x ^{900} + x ^{90} + x ^{6} + \frac{1}{x} + .... + \frac{1}{x}}{2000} \geq 1

Hence

x^{1000} + x^{900} + x^{900} + x^{6} + \frac{1996}{x} \geq 2000

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Question Text	If x > 0, then the minimum value of $x^{1000} + x^{900} + x^{90} + x^{6} + \frac{1996}{x}$ is
Answer Type	Text solution:1
Upvotes	150

If x > 0, then the minimum value of x1000+x900+x90+x6+x1996​ is

Text solutionVerified

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If x > 0, then the minimum value of $x^{1000} + x^{900} + x^{90} + x^{6} + \frac{1996}{x}$ is