What is the correct notation for non simultaneous (asynchronous) equations?most common practice is when we type simultaneous equations in form like that:{x+y=2x−y=2But, what if have equation likex4−5x2+6=0and i want to denote it into 2 equations:x2=2and&nbsp;x2=3

Question

What is the correct notation for non simultaneous (asynchronous) equations?most common practice is when we type simultaneous equations in form like that:{x+y=2x−y=2But, what if have equation likex4−5x2+6=0and i want to denote it into 2 equations:x2=2and&amp;nbsp;x2=3

Wernbergbo9d · Accepted Answer

Also in the first example, we can write both equations also as one equation&amp;nbsp;(x+y−2)(x−y−2)=0. However, the system of two equations need not be equivalent to the one given equation, i.e.,&amp;nbsp;x4−5x2+6=0&amp;nbsp;is not equivalent to&amp;nbsp;x2−2=0&amp;nbsp;and&amp;nbsp;x2−3=0, since&amp;nbsp;(x2−2)(x2−3)=0&amp;nbsp;only implies that one factor must be zero, but not both.In general, we have here systems of (polynomial) equations. For example,xy2z+27xz4−y5=0x3yz−xyz+20=0xy3z+xz2+x+y+z=0A solution has to satisfy all equations simultaneously. Your systems arex+y−2=0,x−y−2=0,and&amp;nbsp;(x^2-2)(x^2-3)&amp;nbsp;=0

What is the correct notation for non simultaneous (asynchronous) equations? most common practice

Answered question

Answer & Explanation

New Questions in Algebra I