2.
√3x + 7 + √x + 1 =2

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

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Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

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6/20

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