Question

[thủy nguyễn]

So sánh: 75²⁰⁰⁵ - 75²⁰⁰⁴ và 75²⁰⁰⁴ - 75²⁰⁰³

Answer 1

[Mashiro Shiina]

Ta có:

\(VT=75^{2005}-75^{2004}\)

\(VT=75^{2004}.75-75^{2004}.1\)

\(VT=75^{2004}\left(75-1\right)\)

\(VT=75^{2004}.74\)

\(VP=75^{2004}-75^{2003}\)

\(VP=75^{2003}.75-75^{2003}.1\)

\(VP=75^{2003}\left(75-1\right)\)

\(VP=75^{2003}.74\)

\(VT>VP\)

Answer 2

[Mới vô]

\(75^{2005}-75^{2004}=75^{2004}\cdot\left(75-1\right)=75^{2004}\cdot74\\ 75^{2004}-75^{2003}=75^{2003}\cdot\left(75-1\right)=75^{2003}\cdot74\\ \text{Vì }75^{2004}>75^{2003}\text{ nên }75^{2004}\cdot74>75^{2003}\cdot74\Leftrightarrow75^{2005}-75^{2004}>75^{2004}-75^{2003}\)