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In a triangle A B C prove that a//(a+c)...

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

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.

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

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

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

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

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

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

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  8. 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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  9. If (log)2(a+b)+(log)2(c+d)geq4. Then find the minimum value of the exp...

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

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  12. Prove that b^2c^2+c^2a^2+a^2b^2> a b cxx(a+b+c)(a ,b ,c >0) .

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

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

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

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

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

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

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

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  20. 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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