Question

Solve: √2x-8= √x+4 the equation.​

Answer 1

(a) x = 12

Explanation:

The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.

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square

`\left(√(2x-8)\right)^2=\left(√(x+4)\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}`

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Additional comment

You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.