SOLUTION: If g(x) = √( x - 1) + √(2x), find all values of x for which g(x) = 6

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Question 245970: If g(x) = √( x - 1) + √(2x), find all values of x for which g(x) = 6
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
sqrt(x-1)+sqrt(2x)=6
sqrt(x-1)=6-sqrt(2x)
x-1=2x-12sqrt(2x)+36
-x-37=-12sqrt(2x)
x^2+74x+1369=288x square each side
x^2-214x+1369=0
x=6.60... The other answer is extraneous.
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=40320 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 207.399203184089, 6.60079681591094. Here's your graph:
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