Question 79040
{{{sqrt(x-1)=x-3}}}


{{{(sqrt(x-1))^2=(x-3)^2}}} Square both sides


{{{x-1=(x-3)^2}}}


{{{x-1=x^2-6x+9}}} Foil the right side


{{{0=x^2-7x+10}}} Get all terms to one side

Use the quadratic formula to solve for x

*[invoke quadratic "x", 1, -7, 10 ]

So we get 2 possible solutions:

x=2, x=5

However, we need to check whether or not they work

Plug in x=2

{{{sqrt(2-1)=2-3}}}
{{{sqrt(1)=-1}}}
{{{1=-1}}} Since this is not true, we must discard this possible solution

Plug in x=5

{{{sqrt(5-1)=5-3}}}
{{{sqrt(4)=2}}}
{{{2=-2}}} Since this answer works, this is the only solution

So our answer is 

{{{x=5}}}

Notice the 2 graphs only intersect at one spot, which is (5,2)

{{{ graph( 300, 200, -2, 10, -10, 10, x-3, sqrt(x-1)) }}}