First slide

Means - A.M/G.M/H.M

Question

$If a, b, c are the sides of a triangle then \frac{a}{b + c - a} + \frac{b}{c + a - b} + \frac{c}{a + b + c}$

Moderate

A

$\leq 3$
B

$\geq 3$
C

$\leq 2$
D

$\geq 2$

Solution

If a, b, c are the sides of triangle the
$\begin{array}{l} b + c - a > 0, c + a - b > 0, a + b - c > 0 \\ x = b + c - a, y = c + a - b, z = a + b + c \\ Now, \frac{a}{b + c - a} + \frac{b}{c + a - b} + \frac{c}{a + b + c} = \frac{y + z}{2 x} + \frac{z + x}{2 y} + \frac{x + y}{2 z} \geq 3 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App