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Prove that a^4+b^4+c^4>abc(a+b+c). [a,b,...

Prove that `a^4+b^4+c^4>abc(a+b+c).` [a,b,c are distinct positive real number]..

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

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  2. If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

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  3. Prove that a^4+b^4+c^4>abc(a+b+c). [a,b,c are distinct positive real n...

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  4. Prove that the greatest value of x y is c^3/sqrt(2a b), if a^2x^4+b^2y...

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  5. If y = sin^-1(10x) + pi/2 then find the value of dy/dx .

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  6. If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

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  7. If x and y are positive real numbers and m, n are any positive integ...

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  8. The least value of the expression 2(log)(10)x-(log)x(0. 01),forx >1, i...

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  9. If a,b,c are positive real no., then prove that [(1+a)(1+b)(1+c)]^7 g...

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  10. True / False For every intger n >1 , the inequality (n !)^(1//n)<(n+1)...

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  11. If x ,y in R^+ satisfying x+y=3, then the maximum value of x^2y is.

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  12. For anyx ,y , in R^+,x y >0 . Then the minimum value of (2x)/(y^3)+(x...

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  13. If a ,b ,a n dc are positive and 9a+3b+c=90 , then the maximum value o...

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  14. Given that x ,y ,z are positive real such that x y z=32. If the minimu...

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  15. If the product of n positive numbers is n^n , then their sum is (a)...

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  16. If a,b,c are different positive real numbers such that b+c−a,c+a−b and...

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  17. Find the greatest value of x^2 y^3, where x and y lie in the first qua...

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  18. Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and ...

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  19. If a1, a2,...... ,an >0, then prove that (a1)/(a2)+(a2)/(a3)+(a3)/(a4...

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  20. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

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