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The ubiquitous AM-GM inequality has many...

The ubiquitous AM-GM inequality has many
applications. It almost crops up in unlikely situations and
the solutions using AM-GM are truly elegant . Recall
that for n positive reals `a_(i) I = 1,2 …,`n, the AM-GM inequality tells
`(overset(n) underset(1)suma_i)/n ge ( overset(n)underset(1)proda_i)^((1)/(n))`
The special in which the inequality turns into equality
help solves many problems where at first we seem to
have not informantion to arrive at the answer .
If the equation `x^(4) - 4x^(3) + ax^(2) + bx + 1 = 0 ` has
four positive roots , then the value of `(|a|+|b|)/(a+b)` is

A

5

B

`-5`

C

`3`

D

`-3`

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Knowledge Check

  • The ubiquitous AM-GM inequality has many applications. It almost crops up in unlikely situations and the solutions using AM-GM are truly elegant . Recall that for n positive reals a_(i) I = 1,2 …, n, the AM-GM inequality tells (overset(n) underset(1)suma_i)/n ge ( overset(n)underset(1)proda_i)^((1)/(n)) The special in which the inequality turns into equality help solves many problems where at first we seem to have not informantion to arrive at the answer . The number of ordered pairs (x,y) pf real numbers satisfying the equation x^(8) + 6= 8 |xy|-y^(8) is

    A
    10
    B
    8
    C
    4
    D
    2

  • The ubiquitous AM-GM inequality has many applications. It almost crops up in unlikely situations and the solutions using AM-GM are truly elegant . Recall that for n positive reals a_(i) I = 1,2 …, n, the AM-GM inequality tells (overset(n) underset(1)suma_i)/n ge ( overset(n)underset(1)proda_i)^((1)/(n)) The special in which the inequality turns into equality help solves many problems where at first we seem to have not informantion to arrive at the answer . If a,b,c are positive integers satisfying (a)/(b+c)+(b)/(c+a) + (c)/(a+b) = (3)/(2) , then the value of abc + (1)/(abc)

    A
    Is `(85)/(4)`
    B
    Is `(17)/(4)`
    C
    Is `(65)/(8)`
    D
    Can't be determined

  • overset(3)underset(n=1)Sigma tan^(-1) 1/n =

    A
    0
    B
    `pi//2`
    C
    `pi`
    D
    none

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