solve x^4 - 6x^2 = 7

sanman777 · Postby **sanman777** » Mon Mar 23, 2009 4:31 pm

solve x^4-6x^2=7

stapel_eliz · Postby **stapel_eliz** » Mon Mar 23, 2009 5:01 pm

sanman777 wrote:solve x^4-6x^2=7

This is an equation in the form of a quadratic:

. . . . . $x^4\, -\, 6x^2\, -\, 7\, =\, 0$

. . . . . $(x^2)^2\, -\, 6(x^2)\, -\, 7\, =\, 0$

So factor the above just as you would factor the below:

. . . . . $y^2\, -\, 6y\, -\, 7\, =\, 0$

Then solve the two factors:

. . . . . $x^2\, +\, 1\, =\, 0\, \mbox{ or }\, x^2\, -\, 7\, =\, 0$

Whether you have two solutions or four will depend upon whether you've studied complex numbers yet. :wink:

If you get stuck, please reply with a clear listing of your work and reasoning so far. Thank you!

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solve x^4 - 6x^2 = 7

solve x^4 - 6x^2 = 7