Question

$x+\frac{20}{x}-12=0$

Answer 1

Given: $x+\frac{20}{x}-12=0$

On multiplying both sides by x, we get:

x² + 20 – 12x = 0

$\Rightarrow$x² – 12x + 20 = 0

On splitting the middle term –12x as –10x – 2x, we get:

x² – 10x – 2x + 20 = 0

$\Rightarrow$x(x – 10) – 2(x – 10) = 0

$\Rightarrow$(x – 10) (x – 2) = 0

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,

x – 10 = 0 or x – 2 = 0

$\Rightarrow$x = 10 or x = 2

Therefore, the solution of the given equation is x = 10, 2.