Question 1058312
.
Solve. (Enter your answers as a comma-separated list.)

t^4-13t^2+42=0
~~~~~~~~~~~~~~~~~~~~


<pre>
{{{t^4-13t^2+42}}} = {{{0}}}.

Factor the left side

{{{(t^2-6)*(t^2-7)}}} = {{{0}}}.

This equation deploys in two independent equations:


1.  {{{t^2-6}}} = {{{0}}}  --->  {{{t^2}}} = 6  --->  t = +/-{{{sqrt(6)}}}

and

2.  {{{t^2-7}}} = {{{0}}}  --->  {{{t^2}}} = 7  --->  t = +/-{{{sqrt(7)}}}.


<U>Answer</U>.  The solutions of the original equation are {{{sqrt(6)}}}, {{{-sqrt(6)}}}, {{{sqrt(7)}}}, and {{{-sqrt(7)}}}.
</pre>