Решить систему:[tex]x(1 + \frac{y}{100} ) = 2220 \\ (x + 200)(1 + \frac{y - 1}{100} ) = 2420[/tex]. Created by Vee340. algebra-ru

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Vee340 @Vee340

July 2022 1 18 Report

Решить систему:
[tex]x(1 + \frac{y}{100} ) = 2220 \\ (x + 200)(1 + \frac{y - 1}{100} ) = 2420[/tex]

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Regent1828

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$\displaystyle \left \{ {{(x(1+\frac{y}{100}) =2220}\atop {(x+200)(1+\frac{y-1}{100})=2420}} \right.\\\\\left \{{{x=2220:(1+0,01y)}\atop {(2220:(1+0,01y)+200)(1+0,01(y-1))=2420}} \right.\\\\(\frac{2220}{1+0,01y} +200)(1+0,01(y-1))=2420\\\\ \frac{(2220+200+2y)(1+0,01y-0,01)}{1+0,01y}=2420\\\\\\(2420+2y)(0,01y+0,99)=2420+24,2y\\24,2y+0,02y^{2}+2395,8+1,98y-2420-24,2y=0\\0,02y^{2}+1,98y-24,2=0\\y^{2}+99y-1210=0\\\\D= b^{2}-4ac=9801+4840=121^{2}\\\\y_{1,2}= \frac{-bб \sqrt{D}}{2a}\\\\y_{1}=11 \\y_{2}=-110$
$\displaystyle x_{1}=2220:(1+0,01*11)=2000 \\ x_{2}=2220:(1+0,01*(-110))=-22200$

Ответ: {2000; 11}, {-22200; -110}

2 votes Thanks 2

Vee340 Спасибо большое

Regent1828 Да не за что..)) Обращайтесь.

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