x^2=6x/(5-x) What is the sum of the roots of the above equation? Question x^2=6x/(5-x) What is the sum of the roots of the above equation? in progress 0 Math Alice 2 weeks 2021-09-12T05:02:11+00:00 2021-09-12T05:02:11+00:00 1 Answer 0

## Answers ( )

Answer:x = 3 or x = 2 or x = 0 thus: 5Step-by-step explanation:Solve for x over the real numbers:

x^2 = (6 x)/(5 – x)

Cross multiply:

x^2 (5 – x) = 6 x

Expand out terms of the left hand side:

5 x^2 – x^3 = 6 x

Subtract 6 x from both sides:

-x^3 + 5 x^2 – 6 x = 0

The left hand side factors into a product with four terms:

-x (x – 3) (x – 2) = 0

Multiply both sides by -1:

x (x – 3) (x – 2) = 0

Split into three equations:

x – 3 = 0 or x – 2 = 0 or x = 0

Add 3 to both sides:

x = 3 or x – 2 = 0 or x = 0

Add 2 to both sides:

Answer: x = 3 or x = 2 or x = 0