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Prove that (a b+x y)(a x+b y)>4a b x y(a...

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

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

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  2. Find the minimum value of 4sin^(2)x+4cos^(2)x .

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

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

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  5. If a1,a2,.....an are positive real number whose product is a fixed num...

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  6. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

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

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

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  9. In triangle A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq...

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  10. Prove that in A B C ,tanA+tanCgeq3sqrt(3,) where A , B , C are circle...

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  11. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

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

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

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

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

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

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

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