Find all real solutions of the equation x4−8x2+2=0
x4−8x2+2=0w2−8w+2=0Let w=x2w2−8w=−2Subtract 2w2−8w+16=−2+16Complete the square: Add (−82)2=16(w−4)2=14Perfect Square(w−4)=±√14Take the square rootw=4±√14Add 4w=4+√14 and w=4−√14Solve for wx2=4+√14 and x2=4−√14Substitute w=x2x=±√4+√14 and x=±√4−√4Take the square root
Thus, the solutions are
x=√4+√14,x=−√4+√14,x=√4−√14, and x=−√4−√14
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