SOLUTION: Find the real solutions of the given equation. Use a calculator to express solutions rounded to two decimal places.
{{{x^4 + sqrt(2)x^2 - 2 = 0}}}
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Question 1208849: Find the real solutions of the given equation. Use a calculator to express solutions rounded to two decimal places.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Make the "change of variable" and turn the equation into the quadratic equation
Then you could use the quadratic formula that says that the solutions to
are given by
For the equation above , , and
You get (rounded), and
(rounded)
At this point, if as I suspect you were not taught about complex and imaginary numbers, you can only list real solutions.
Then, has no real solutions, and your solutions would be
and
NOTE:
If you are not fond of the quadratic formula, "completing the square" would be an option,
if you were taught to transform something like
into , add to both sides
to get ,
rewrite it as and for the solutions
and
They really quote that formula as for ,
but the name/letter used for the variable makes no difference.
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