# How to solve the system of equation with three variables

## System of equation with three variables

Find the value of **x⁻¹ + y⁻¹ + z⁻¹** when the system of equation with three variables are, **x + y + z = 7**, **x² + y² + z² = 9** and** x y z = 5**

## Solution

We know

(x + y + z)**²** = x**²** + y**²** + z**²** + 2xy + 2yz + 2xz

⇒ 7**²** = 9 + 2(xy + yz + xz)

⇒ 40 = 2(xy + yz + xz)

so, xy + yz + xz = 20

divided with **x y z** then

(xy + yz + xz) / (x y z) = 20/5

⇒ z⁻¹ + x⁻¹ + y⁻¹ = 4

Then the value of **x⁻¹ + y⁻¹ + z⁻¹ **is** 4**