<prompt> Pata jumla ya thamani kamili za mizizi ya x4-4x3-4x216x-80.  <response>: anzaalignx4-4x3-4x216x-8x4-4x34x2-8x2-16x8x2x-22-8x-12x2-2x2-2sqrt2x-2sqrt22x2-22sqrt2x2sqrt2x2-2-2sqrt2x-2sqrt2 .endalignLakini kwa kutambua kwamba 1sqrt2232sqrt2 na kukamilisha mraba, beginalignx2-22sqrt2x2sqrt2 x2-22sqrt2x32sqrt2-3 x-1sqrt22-sqrt32x-1-sqrt2sqrt3x-1-sqrt2-sqrt3.mwishoalignVivyo hivyo, anzaalignx2-2-2sqrt2x-2sqrt2x-1sqrt2sqrt3x-1sqrt2 -sqrt3,endalignkwa hivyo mizizi ya quartic ni 1pmsqrt2pmsqrt3. Moja tu kati ya hizi ni hasi, yaani 1-sqrt2-sqrt3, kwa hivyo jumla ya thamani kamili za mizizi ni 1sqrt2sqrt3 1sqrt2-sqrt31-sqrt2sqrt3-1-sqrt2-sqrt3 22sqrt22sqrt3. 