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Resolver I (complex solution)
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Resolver I
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Resolver R (complex solution)
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IRR\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Multiplica ambos lados da ecuación por \left(r+1\right)^{2}.
IR^{2}\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Multiplica R e R para obter R^{2}.
IR^{2}\left(r^{2}+2r+1\right)=22000+\left(r+1\right)^{2}\left(-18000\right)
Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(r+1\right)^{2}.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Usa a propiedade distributiva para multiplicar IR^{2} por r^{2}+2r+1.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r^{2}+2r+1\right)\left(-18000\right)
Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(r+1\right)^{2}.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000-18000r^{2}-36000r-18000
Usa a propiedade distributiva para multiplicar r^{2}+2r+1 por -18000.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=4000-18000r^{2}-36000r
Resta 18000 de 22000 para obter 4000.
\left(R^{2}r^{2}+2R^{2}r+R^{2}\right)I=4000-18000r^{2}-36000r
Combina todos os termos que conteñan I.
\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I=4000-36000r-18000r^{2}
A ecuación está en forma estándar.
\frac{\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I}{R^{2}r^{2}+2rR^{2}+R^{2}}=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}
Divide ambos lados entre R^{2}r^{2}+2rR^{2}+R^{2}.
I=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}
A división entre R^{2}r^{2}+2rR^{2}+R^{2} desfai a multiplicación por R^{2}r^{2}+2rR^{2}+R^{2}.
I=\frac{2000\left(2-18r-9r^{2}\right)}{R^{2}\left(r+1\right)^{2}}
Divide 4000-36000r-18000r^{2} entre R^{2}r^{2}+2rR^{2}+R^{2}.
IRR\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Multiplica ambos lados da ecuación por \left(r+1\right)^{2}.
IR^{2}\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Multiplica R e R para obter R^{2}.
IR^{2}\left(r^{2}+2r+1\right)=22000+\left(r+1\right)^{2}\left(-18000\right)
Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(r+1\right)^{2}.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)
Usa a propiedade distributiva para multiplicar IR^{2} por r^{2}+2r+1.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r^{2}+2r+1\right)\left(-18000\right)
Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(r+1\right)^{2}.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000-18000r^{2}-36000r-18000
Usa a propiedade distributiva para multiplicar r^{2}+2r+1 por -18000.
IR^{2}r^{2}+2IR^{2}r+IR^{2}=4000-18000r^{2}-36000r
Resta 18000 de 22000 para obter 4000.
\left(R^{2}r^{2}+2R^{2}r+R^{2}\right)I=4000-18000r^{2}-36000r
Combina todos os termos que conteñan I.
\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I=4000-36000r-18000r^{2}
A ecuación está en forma estándar.
\frac{\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I}{R^{2}r^{2}+2rR^{2}+R^{2}}=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}
Divide ambos lados entre R^{2}r^{2}+2rR^{2}+R^{2}.
I=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}
A división entre R^{2}r^{2}+2rR^{2}+R^{2} desfai a multiplicación por R^{2}r^{2}+2rR^{2}+R^{2}.
I=\frac{2000\left(2-18r-9r^{2}\right)}{\left(R\left(r+1\right)\right)^{2}}
Divide 4000-18000r^{2}-36000r entre R^{2}r^{2}+2rR^{2}+R^{2}.