sqrt(x^2 - 5x + 3) = sqrt (x^2 + 4x -1) solve for x

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sqrt(x^2 - 5x + 3) = sqrt(x^2 + 4x - 1)

To solve the equation, first we need to get rid of the square root by squaring both sides:

==>[sqrt(x^2 - 5x + 3) ]^2= [ sqrt(x^2 + 4x -1)]^2

==> (x^2 - 5x + 3 = x^2 + 4x -1

Now eliminate similar terms (x^2)

==> -5x + 3 = 4x -1

No combine like terms:

==> -5x -4x = -1 -3

==> -9x = -4

**==>x= 4/9**

To solve sqrt(x^2-5x+3) = sqrt(x^2+4x-1).

We rearrange this as:

sqrt(x^2-5x+3) -sqrt(x^2+4x-1) = 0.

We rationalise te numerator:

{sqrt(x^2-5x+3)-sqrt(x^2+4x-1}{sqrt(x^2-5x+3)+sqrt(x^2+4x+1}/{sqrt(x^2-5x+3)+sqrt(x^2+4x-1} = 0

(-5x+3-4x-1)/{sqrt(x^2-5x+3)+sqrt(x^2+4x-1} = 0

Multiply both sides by {sqrt(x^2-5x+3)+sqrt(x^2+4x-1} and we get:

-5x+3-4x+1 = 0

-9x+4 = 0.

-9x= -4

x = -2/-9 = 2/9.

Therefor x = 4/9 is the solution.

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