Home
Class 12
MATHS
If p and q are positive real numbers ...

If p and q are positive real numbers such that `p^2+""q^2=""1` , then the maximum value of `(p""+""q)` is (1) 2 (2) 1/2 (3) `1/(sqrt(2))` (4) `sqrt(2)`

Text Solution

AI Generated Solution

To find the maximum value of \( p + q \) given that \( p^2 + q^2 = 1 \) where \( p \) and \( q \) are positive real numbers, we can use the Cauchy-Schwarz inequality or the method of Lagrange multipliers. Here, we will use the Cauchy-Schwarz inequality for simplicity. ### Step-by-step Solution: 1. **Understanding the constraint**: We know that \( p^2 + q^2 = 1 \). 2. **Using the Cauchy-Schwarz Inequality**: ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|6 Videos

Similar Questions

Explore conceptually related problems

Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q^2P , then determinant of (P^2+""Q^2) is equal to (1) 2 (2) 1 (3) 0 (4) 1

Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a nd""P^2Q""=""Q^2P , then determinant of (P^2+""Q^2) is equal to (1) 2(2) 1 (3)0 (4) 1

Knowledge Check

  • If p and q are positive, p^2 + q^2 = 16 , and p^2 - q^2 = 8 , then q =

    A
    2
    B
    4
    C
    8
    D
    `2sqrt(2)`

  • If p + q = 7 and pq = 12 , then will is the value of 1/(p^2) + 1/(q^2) ?

    A
    `1//6`
    B
    `25//144`
    C
    `49//144`
    D
    `7//12`

  • Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

    A
    `(2)/(9)(p-q)(2q-p)`
    B
    `(2)/(9)(q-p)(2p-q)`
    C
    `(2)/(9)(q-2p)(2q-p)`
    D
    `(2)/(9)(2p-q)(2q-p)`

    • Similar Questions

    Explore conceptually related problems

    If 2p=x+1/x and 2q=y+1/y , then the value of ((pq+sqrt((p^2-1)(q^2-1)))/(xy+1/(xy))) is

    if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4 ,then the value of q is (A) 1 (B) 1/sqrt(2) (C) 1/3 (D) 1/2

    For positive real numbers a (a>1) let p_a and q_a , be the maximum and minimum values of log_a(x) , for alt=xlt=2a and if p_a-q_a=1/2 then the value of a is not greater than

    P=x^3-1/x^3, Q=x-1/x x in (1,oo) then minimum value of P/(sqrt(3)Q^2)

    Find the value of : 1/2 p^(2) xx 4p^(2)q xx(-3 p)

    Home
    Profile