so sánh :2^30+3^30+4^30 và 3.(23)^10

Ta có

$2^{30} + 3^{30} + 4^{30} = 2^{3.10} + 3^{3.10} + 4^{3.10}$

$= (2^3)^{10} + (3^3)^{10} + (4^3)^{10}$

$= 8^{10} + 27^{10} + 64^{10}$

Ta có

$8^{10} + 27^{10} + 64^{10} > 8^{10} + 23^{10} + 46^{10}$

$<-> 8^{10} + 27^{10} + 64^{10} > 8^{10} + 23^{10} + (2.23)^{10}$

$<-> 8^{10} + 27^{10} + 64^{10} > 8^{10} + 23^{10} + 2^{10} . 23^{10}$

$<-> 8^{10} + 27^{10} + 64^{10} > 8^{10} + (2^{10}+1) . 23^{10} > 8^{10} + 3.23^{10}$

Vậy ta có $2^{30} + 3^{30} + 4^{30} > 3.(23)^{10}$

Đáp án:

Giải thích các bước giải:

230+330+430=23.10+33.10+43.10230+330+430=23.10+33.10+43.10

=(23)10+(33)10+(43)10=(23)10+(33)10+(43)10

=810+2710+6410=810+2710+6410

Ta có

810+2710+6410>810+2310+4610810+2710+6410>810+2310+4610

<−>810+2710+6410>810+2310+(2.23)10<−>810+2710+6410>810+2310+(2.23)10

<−>810+2710+6410>810+2310+210.2310<−>810+2710+6410>810+2310+210.2310

<−>810+2710+6410>810+(210+1).2310>810+3.2310<−>810+2710+6410>810+(210+1).2310>810+3.2310

Vậy ta có 230+330+430>3.(23)10