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If y z+z x+x y=12 , and x , y , z are p...

If `y z+z x+x y=12 , and x , y , z` are positive values, find the greatest value of `x y zdot`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Let Tr denote the rth term of a G.P. for r=1,2,3, If for some positive...

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  2. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c

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  3. If y z+z x+x y=12 , and x , y , z are positive values, find the great...

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  4. If S=a1+a2+......+an,ai in R^+ for i=1 to n, then prove that S/(S-a1)...

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  5. If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)...

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  6. If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.

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  7. Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

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  8. In a triangle A B C prove that a/(a+c)+b/(c+a)+c/(a+b)<2

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  9. Find the least value of secA+secB+secC in an acute angled triangle.

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  10. Prove that [(n+1)//2]^n >(n !)dot

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  11. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

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  12. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

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  13. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

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  14. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

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  15. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

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

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  17. If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

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

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

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

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