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The minimum value of the sum of real num...

The minimum value of the sum of real number `a^-5,a^-4,3a^-3,1,a^8` and `a^10` with `a > 0` is

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Find the minimum value of 4sin^(2)x+4cos^(2)x .

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  2. Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

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  3. The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and ...

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  4. If a1,a2,------ ,an are positive real numbers whose product is a fixe...

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  5. If a ,b ,c ,d are positive real umbers such that a+b+c+d=2,then M=(a+...

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  6. A straight line through the vertex P of a triangle P Q R intersects th...

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  7. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

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  8. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

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  9. In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e...

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  10. If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+...

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  11. 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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  12. Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

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

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

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

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

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  17. If Cr=(n !)/([r !(n-r)]), the prove that sqrt(C1)+sqrt(C2)+.......sq...

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

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

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  20. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

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