Question

1) Tính giá trị

\(A=\frac{1}{3589}.7\frac{1}{297}-3\frac{3588}{3589}.\frac{2}{297}-\frac{7}{3589}-\frac{3}{3589.297}\)

2) So sánh

\(A=999994.999999.999992-999996.999991.999998\)

\(B=444443.444448.444441-444445.444440.444447\)

 

 

Answer 1

Thay  999990=a vào biểu thức A ta được

\(A=\left(a+4\right)\left(a+9\right)\left(a+2\right)-\left(a+6\right)\left(a+1\right)\left(a+8\right)\)

\(=\left(a^2+13a+36\right)\left(a+2\right)-\left(a^2+7a+6\right)\left(a+8\right)\)

\(=a^3+2a^2+13a^2+26a+36a+72-a^3-8a^2-7a^2-56a-6a-48\)

\(=24\)

Thay b=44440 vào B ta được

\(B=\left(b+3\right)\left(b+8\right)\left(b+1\right)-\left(b+5\right)b\left(b+7\right)\)

\(=\left(b^2+11b+24\right)\left(b+1\right)-\left(b^2+5b\right)\left(b+7\right)\)

\(=b^3+b^2+11b^2+11b+24b+24-b^3-7b^2-5b^2-35b\)

\(=24\)

Vậy A=B (=24)