If x is a whole number and 437 = (21 + x)(21 - x), then x =

Answer:2Step-by-step explanation:In general, [tex](a+b)(a-b)=a^2-b^2[/tex].So we have here that: [tex]437=21^2-x^2[/tex][tex]437=441-x^2[/tex]We went [tex]-x^2[/tex] by itself first.Subtract 441 on both sides:[tex]437-441=-x^2[/tex][tex]-4=-x^2[/tex]Multiply both sides by -1:[tex]4=x^2[/tex]Take the square root of boht sides:[tex]\pm \sqrt{4}=x[/tex][tex]\pm 2=x[/tex]So both 2 and -2 would satisfy the equation.Only one of these is a whole number.The whole numbers consist of the elements that you can count with and 0.The whole number set is {0,1,2,3,4,5,6,7,...}So 2 is the answer.Check:Replace x with 2:437=(21+2)(21-2)437=(23)(19)437=437 is a true equation so 2 is definitely a solution.