Answer:
-22, -23 are two consecutive negative numbers whose product is 506
Step-by-step explanation:
Let x, x+1 are two consecutive negative numbers
According to given Condition
[tex](x)(x+1) = 506[/tex]
[tex]x^{2} +x = 506[/tex]
[tex]x^{2} +x - 506=0[/tex]
[tex]x^{2} +22x -23x- 506=0[/tex]
[tex](x^{2} +22x) -(23x+ 506)=0[/tex]
[tex]x(x +22) -23(x+ 22)=0[/tex]
[tex](x +22) (x-23)=0[/tex]
[tex]x+22 =0[/tex] or [tex]x-23=0[/tex]
[tex]x=-22[/tex] or [tex]x=23[/tex]
As Number is negative so x = -22
x+1 = -23
-22, -23 are two consecutive negative numbers whose product is 506
21 and 22 are two consecutive numbers whose squares, when subtracted, equals 43.
