SOLUTION: Solve a) x^4 + x^2 - 6 = 0 Can you please help me out? Thanks so much in advance:)

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Question 812941: Solve
a) x^4 + x^2 - 6 = 0

Can you please help me out? Thanks so much in advance:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z = x^2. So z^2 = x^4 (square both sides)

+x%5E4+%2B+x%5E2+-+6+=+0+

+z%5E2+%2B+z+-+6+=+0+ Replace z with x^2 and x^4 with z^2

+%28z+-+2%29%28z+%2B+3%29+=+0+

+z+-+2+=+0 or z+%2B+3+=+0+

+z+=+2 or z+=+-3+

+x%5E2+=+2 or x%5E2+=+-3+ Remember we let z = x^2, so make the proper replacement

+x+=+%22%22%2B-sqrt%282%29 or x+=+%22%22%2B-sqrt%28-3%29+

+x+=+sqrt%282%29, +x+=+-sqrt%282%29, x+=+i%2Asqrt%283%29+ or x+=+-i%2Asqrt%283%29+


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The four solutions are

+x+=+sqrt%282%29, +x+=+-sqrt%282%29, x+=+i%2Asqrt%283%29+ or x+=+-i%2Asqrt%283%29+

Note: i is the imaginary number i+=+sqrt%28-1%29