Question

If x, y, z are distinct positive real numbers then the expression below would be $\frac{x^2(y+z)+y^2(x+z)+z^2(x+y)}{xyz}$

• A. Greater than 4
• B. Greater than 5
• C. Greater than 6
• D. Less than 6

Answer 1

The correct option is C Greater than 6

Here x,y and z are distinct positive real number.

So,$\frac{x^2(y+z)+y^2(x+z)+z^2(x+y)}{xyz}$

$=\frac{x}{y}+\frac{x}{z}+\frac{y}{x}+\frac{y}{z}+\frac{z}{x}+\frac{z}{y}$

$=(\frac{x}{y}+\frac{y}{x})+(\frac{y}{z}+\frac{z}{y})+(\frac{z}{x}+\frac{x}{z})$

($\frac{a}{b}+\frac{b}{a}>2$ if a $\&$ b are distinct numbers.)

$\Rightarrow$ 2+2+2

$\Rightarrow$ 6

Hence option (c)