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Simplifying xy + xz + xt + yz + yt + zt = x2 + y2 + z2 + t2 Reorder the terms: tx + ty + tz + xy + xz + yz = x2 + y2 + z2 + t2 Reorder the terms: tx + ty + tz + xy + xz + yz = t2 + x2 + y2 + z2 Solving tx + ty + tz + xy + xz + yz = t2 + x2 + y2 + z2 Solving for variable 't'. Reorder the terms: tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = t2 + x2 + y2 + z2 + -1t2 + -1x2 + -1y2 + -1z2 Reorder the terms: tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = t2 + -1t2 + x2 + -1x2 + y2 + -1y2 + z2 + -1z2 Combine like terms: t2 + -1t2 = 0 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = 0 + x2 + -1x2 + y2 + -1y2 + z2 + -1z2 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = x2 + -1x2 + y2 + -1y2 + z2 + -1z2 Combine like terms: x2 + -1x2 = 0 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = 0 + y2 + -1y2 + z2 + -1z2 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = y2 + -1y2 + z2 + -1z2 Combine like terms: y2 + -1y2 = 0 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = 0 + z2 + -1z2 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 tx + ty + tz + -1t2 + xy + xz + -1x2 + yz + -1y2 + -1z2 = 0 The solution to this equation could not be determined.
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