ВОТ ПОМОГИТЕ.............. Created by malgosi35. matematika-ru

ВОТ ПОМОГИТЕ...

malgosi35 @malgosi35

August 2022 1 12 Report

ВОТ ПОМОГИТЕ.............

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xERISx

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$\dfrac{4007^3-2003^3-2004^3}{2003\cdot 2004\cdot 4007}= \\ \\ =\dfrac{(4007-2003)(4007^2+4007\cdot 2003 + 2003^2)-2004^3}{2003\cdot 2004\cdot 4007}=\\ \\ =\dfrac{2004\cdot (4007^2+4007\cdot 2003 + 2003^2-2004^2)}{2003\cdot 2004\cdot 4007}=\\ \\ =\dfrac{4007^2+4007\cdot 2003 + 2003^2-2004^2}{2003\cdot 4007}=\\ \\ =\dfrac{(4007-2004)(4007+2004)+4007\cdot 2003 + 2003^2}{2003\cdot 4007}=\\ \\ =\dfrac{2003\cdot 6011+4007\cdot 2003 + 2003^2}{2003\cdot 4007}=$

$=\dfrac{2003\cdot (6011+4007+ 2003)}{2003\cdot 4007}= \\ \\ =\dfrac{6011+4007+ 2003}{4007}=\dfrac{12021}{4007}=\boldsymbol{3}$

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Использованы формулы

a³ - b³ = (a - b)(a² + ab - b²)

a² - b² = (a - b)(a + b)

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