Question 1207658
<pre>
Find the real solutions of the equation. 

(5x^2 - 6)^(1/4) = x

I found x to be -sqrt{6} and sqrt{6}.

The textbook answer is x = sqrt{2} and x = sqrt{3}.

Help.

Your answers are WRONG, but because you failed to show your work, no-one can determine where you made
your mistake.

        {{{matrix(1,3, (5x^2 - 6)^(1/4), "=", x)}}}
Note that the left-side of the equation is being raised to a power ({{{1/4}}}), so the right-side (x), CANNOT 
be negative (< 0). This will determine the correct answers.

        {{{matrix(1,3, (5x^2 - 6)^(1/4), "=", x)}}}
   {{{matrix(1,3, ((5x^2 - 6)^(1/4))^4, "=", x^4)}}} ---- Raising each side to the 4<sup>th</sup> power
{{{matrix(3,3, ((5x^2 - 6)^(1/cross(4)))^cross(4), "=", x^4, 5x^2 - 6, "=", x^4, 0, "=", x^4 - 5x^2 + 6)}}}
                  0 = (x<sup>2</sup> - 3)(x<sup>2</sup> - 2)
               {{{matrix(4,3, 0, "=", x^2 - 3, 3, "=", x^2, " "+- sqrt(3), "=", sqrt(x^2), " "+- sqrt(3), "=", x)}}}         {{{matrix(4,3, 0, "=", x^2 - 2, 2, "=", x^2, " "+- sqrt(2), "=", sqrt(x^2), " "+- sqrt(2), "=", x)}}} 

As stated earlier, the right-side of the equation CANNOT be negative (< 0), so {{{highlight_green(system(matrix(2,3, highlight(sqrt(3)), "=", highlight(x), highlight(sqrt(2)), "=", highlight(x))))}}}</pre>