How do you solve #x^ { 4} = 10+ 3x ^ { 2}#?

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Answer 1 · 2017-04-02T02:31:25

#x=+-sqrt5#

#x^4=10+3x^2#

#x^4-3x^2-10=0#

Let #color(green)(u=x^2)#

#color(green)(u^2-3u-10=0)#

Factor like a quadratic:
#color(green)((u-5)(u+2)=0)#

#color(green)(u=5, u=-2)#

#x^2=5, color(red)(x^2=-2)#

#x=+-sqrt5#