Home
Class 12
MATHS
Show that the minimum value of (x+a)(x+b...

Show that the minimum value of `(x+a)(x+b)//(x+c)dotw h e r ea > c ,b > c ,` is `(sqrt(a-c)+sqrt(b-c))^2` for real values of `x >-cdot`

Text Solution

AI Generated Solution

To show that the minimum value of the expression \(\frac{(x+a)(x+b)}{(x+c)}\) is \((\sqrt{a-c} + \sqrt{b-c})^2\) for \(x > -c\), where \(a > c\) and \(b > c\), we can follow these steps: ### Step 1: Rewrite the Expression We start with the expression: \[ y = \frac{(x+a)(x+b)}{(x+c)} \] Let \(y = x + c\). Then, we can express \(x\) as: ...
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise ILLUSTRATION|122 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

Similar Questions

Explore conceptually related problems

Show that the minimum value of (x+a)(x+b)//(x+c) where a > c ,b > c , is (sqrt(a-c)+sqrt(b-c))^2 for real values of x > -c .

Prove that the minimum value of ((a+x)(b+x))/((c+x))a ,b > c ,x >-c is (sqrt(a-c)+sqrt(b-c))^2

Find the minimum value of a x+b y , where x y=c^2 and a ,\ b ,\ c are positive.

Evaluate: int(a x^2+b x+c)/((x-a)(x-b)(x-c))\ dx ,\ \ w h e r e\ a ,\ b ,\ c are distinct.

Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers a ,b ,c) is (a) 1 (b) 2 (c) 4 (d) 6

The minimum value of [x_1-x_2)^2 + ( 12 - sqrt(1 - (x_1)^2)- sqrt(4 x_2)]^(1/2) for all permissible values of x_1 and x_2 is equal to asqrtb -c where a,b,c in N , the find the value of a+b-c

If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roots, then p can be (sqrt(a)-sqrt(b))^2 b. (sqrt(a)+sqrt(b))^2 c. a+b d. a-b

Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c 0 c. a b >0 d. a b c<0

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot