SOLUTION: Please help me solve this equation: x^8-20x^4+64=0

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Question 730422: Please help me solve this equation: x^8-20x^4+64=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E8+-+20x%5E4+%2B+64+=+0+
Let +z%5E2+=+x%5E8+
and +z+=+x%5E4+
+z%5E2+-+20z+%2B+64+=+0+
+%28+z+-+4+%29%2A%28+z+-+16+%29+ ( just figured it out )
+z+=+4+
+z+=+16+
so
+x%5E4+=+4+
+x%5E2+=+2+
+x%5E2+=+-2+
and
+x%5E4+=+16+
+x%5E2+=+4+
+x%5E2+=+-4+
-------------
Solving for +x+,
(1) +x+=+sqrt%282%29+
(2) +x+=+-sqrt%282%29+
(3) +x+=+sqrt%282%29%2Ai+
(4) +x+=+-sqrt%282%29%2Ai+
----------------
(5) +x+=+2+
(6) +x=+-2+
(7) +x+=+2i+
(8) +x+=+-2i+
The 8 roots are labeled (1) - (8)
---------------------------
I'll check one of them
(4) +x+=+-sqrt%28-2%29+
+x%5E8+-+20x%5E4+%2B+64+=+0+
+%28+-sqrt%28-2%29++%29%5E8+-+20%2A%28+-sqrt%28-2%29+%29%5E4+%2B+64+=+0+
+16%2Ai%5E8+-+20%2A4%2Ai%5E4+%2B+64+=+0+
+16%2A%28-1%29%5E4+-+80%2A%28-1%29%5E2+%2B+64+=+0+
+16+-+80+%2B+64+=+0+
+0+=+0+
OK
You can check the rest