How do you solve $\sqrt{6 x - 8} = x$ $sqrt(6x - 8) = x$ ?

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Answer 1 · 2017-10-02T20:48:28

$x = 2$ $x = 2" "$ or $x = 4$ $" "x = 4$

Given:

$\sqrt{6 x - 8} = x$ $sqrt(6x-8) = x$

Note that $sqrt(...) >= 0$ . So we require $x >= 0$

Square both sides of the given equation (noting that this may introduce extraneous solutions), to get:

$6x-8 = x^2$

Subtract $6x-8$ from both sides to get:

$0 = x^2-6x+8 = (x-4)(x-2)$

So:

$x = 2" "$ or $" "x = 4$

Since these are both positive, they are both solutions of the original equation.

How do you solve sqrt(6x - 8) = x √6x−8=xsqrt(6x - 8) = x ?