how to solve x-8√x+12=0 ?

√x+12 = √(x+12) or √(x)+12 ???

Is the equation x - 8sqrt(x) + 12 = 0?

If so, you can try factoring it:

Start with what you know:

Since the first term in each factor multiplied together is x, that first term must be sqrt(x) .

So far:

[sqrt(x) +- ??] * [sqrt(x) +- ??]

Since the constant 12 is positive, the signs in the factors are the same. Since the middle term is negative, they're minus:

[sqrt(x) - ??] * [sqrt(x) - ??]

Now you need two factors of 12 that add up to 8. The values 2 and 6 meet both of those requirements:

[sqrt(x) - 2] * [sqrt(x) - 6]

The first factor goes to zero when sqrt(x) = 2 which corresponds to x = 4

The second factor goes to zero when sqrt(x) = 6 which corresponds to x = 36

The roots of the equation are 4 and 36.

(√x)^2 - 8(√x) + 12 = 0

or, (√x)^2 - 6√x -2√x +12 = 0

or, (√x-2)(√x-6) = 0

so, √x = 2 or 6

i.e. x= 4 or 36