Solve x.e for sqrt (x^2-3) =  x-5. Solve x.e for sqrt (x^2-3) =  x-5.

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You need raise to square both sides such that:

You need to expand the square to the right such that:

You need to eliminate both sides such that:

You should keep the term that contains x to the right side and you need to move the constant terms to the left side such that:

You need to remember that the value of x is good only if it makes the radicand positive such that:

Hence, the solution to the equation is .

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sqrt (x^2 - 3)  = x-5

First let us square both sides:

[sqrt(x^2-3)]^2 = (x-5)^2

==> (x^2 -3) = x^2 - 10x + 25

Reduce similar :

==> -3 = -10x + 25

==> 10x = 28

Now divide by 10:

==> x = 28/10 = 14/5

==> x= 14/5 = 2.8

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