Home
Class 12
MATHS
Prove that a^p b & q >((a p+b p)/(p+q))^...

Prove that `a^p b & q >((a p+b p)/(p+q))^(p+q)dot`

Text Solution

Verified by Experts

Consider p quantities each point equal to a and q quantities each equal to b. we know that
` A.M. gt G.M. `
`therefore ((a+a+....." to p terms")+(b+b+...."to q terms"))/(p+q)`
` gt [(caxxa.... " to p factors ")(bxxb....."to q factors ")]^((1)/(p+q))`
` rArr (ap+bq)/(p+q)gt (a^pb^q)^((1)/(p+q))`
` rArr ((ap+bq)/(p+q))^(p+q) gt (a^pb^q)` lt
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Concept Application Eexercises 6.4|4 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise EXERCISES (Single Correct answer type)|20 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Concept Application Eexercises 6.2|6 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE ENGLISH|Exercise All Questions|764 Videos

Similar Questions

Explore conceptually related problems

Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

Prove that q^^~p -=~ (q to p)

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0

In Figure P Q || C D and P R || C B. Prove that ( A Q)/(Q D)=(A R)/(R B)dot

Without expanding the determinant prove that: |(0, p-q, p-r), (q-p,0, q-r),(r-p, r-q, 0)|=0

The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that the sum of its (p+q) terms is (p+q)/2{a+b+(a-b)/(p-q)}dot

If the p t h ,\ q t h\ a n d\ r t h terms of a G.P. are a ,\ b ,\ c respectively, prove that: a^((q-r))dot^b^((r-p))dotc^((p-q))=1.

If p and q are two statements , prove that ~( p vee q) -= (~p) ^^ ( ~q )

If in an A.P., the pth term is q\ a n d\ (p+q)^(t h) term is zero then the q^(t h) term is a. -p b. p c. p+q d. p-q

Prove that p x^(q-r)+q x^(r-p)+r x^(p-q)> p+q+r ,where p, q, r are distinct and x!=1.