Question

cho 3 số nguyên a,b,c thõa mãn : \((a-b)^3+\left(b-c\right)^3+\left(c-a\right)^3=210\)tinh giá trị  của biểu thức B =  \(|a-b|+|b-c|+|c-a|\) 

Answer 1

(a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">(a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)

3(a−b)(b−c)(c−a)=210⇔(a−b)(b−c)(c−a)=70" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">3(a−b)(b−c)(c−a)=210⇔(a−b)(b−c)(c−a)=70

a;b;cϵZ→a−b;b−c;c−aϵZ" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">a;b;cϵZ→a−b;b−c;c−aϵZ

→a−b;b−c;c−a" role="presentation" style="border:0px; direction:ltr; display:inline-table; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">→a−b;b−c;c−a là ước của 70

70=(−2)(−5)7" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">70=(−2)(−5)7 (do tổng 3 số này bằng 0)

A=2+5+7=14" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">A=2+5+7=14