Lahenda operatorname{IRR}=22000/(1+r)^2-18000

$$\operatorname { IRR } = \frac { 22000 } { ( 1 + r ) ^ { 2 } } - 18000$$

Lahendage ja leidke I (complex solution)

$$\left\{\begin{matrix}I=-\frac{2000\left(9r^{2}+18r-2\right)}{\left(R\left(r+1\right)\right)^{2}}\text{, }&r\neq -1\text{ and }R\neq 0\\I\in \mathrm{C}\text{, }&\left(r=-\frac{\sqrt{11}}{3}-1\text{ or }r=\frac{\sqrt{11}}{3}-1\right)\text{ and }R=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled \left(r+1\right)^{2}-ga.

$$IRR\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Korrutage R ja R, et leida R^{2}.

$$IR^{2}\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage kaksliikme \left(r+1\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$IR^{2}\left(r^{2}+2r+1\right)=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage distributiivsusomadust, et korrutada IR^{2} ja r^{2}+2r+1.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage kaksliikme \left(r+1\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r^{2}+2r+1\right)\left(-18000\right)$$

Kasutage distributiivsusomadust, et korrutada r^{2}+2r+1 ja -18000.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000-18000r^{2}-36000r-18000$$

Lahutage 18000 väärtusest 22000, et leida 4000.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=4000-18000r^{2}-36000r$$

Kombineerige kõik liikmed, mis sisaldavad I.

$$\left(R^{2}r^{2}+2R^{2}r+R^{2}\right)I=4000-18000r^{2}-36000r$$

Võrrand on standardkujul.

$$\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I=4000-36000r-18000r^{2}$$

Jagage mõlemad pooled R^{2}r^{2}+2rR^{2}+R^{2}-ga.

$$\frac{\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I}{R^{2}r^{2}+2rR^{2}+R^{2}}=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}$$

R^{2}r^{2}+2rR^{2}+R^{2}-ga jagamine võtab R^{2}r^{2}+2rR^{2}+R^{2}-ga korrutamise tagasi.

$$I=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}$$

Jagage 4000-36000r-18000r^{2} väärtusega R^{2}r^{2}+2rR^{2}+R^{2}.

$$I=\frac{2000\left(2-18r-9r^{2}\right)}{R^{2}\left(r+1\right)^{2}}$$

Lahendage ja leidke I

$$\left\{\begin{matrix}I=-\frac{2000\left(9r^{2}+18r-2\right)}{\left(R\left(r+1\right)\right)^{2}}\text{, }&r\neq -1\text{ and }R\neq 0\\I\in \mathrm{R}\text{, }&\left(r=-\frac{\sqrt{11}}{3}-1\text{ or }r=\frac{\sqrt{11}}{3}-1\right)\text{ and }R=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled \left(r+1\right)^{2}-ga.

$$IRR\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Korrutage R ja R, et leida R^{2}.

$$IR^{2}\left(r+1\right)^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage kaksliikme \left(r+1\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$IR^{2}\left(r^{2}+2r+1\right)=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage distributiivsusomadust, et korrutada IR^{2} ja r^{2}+2r+1.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r+1\right)^{2}\left(-18000\right)$$

Kasutage kaksliikme \left(r+1\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000+\left(r^{2}+2r+1\right)\left(-18000\right)$$

Kasutage distributiivsusomadust, et korrutada r^{2}+2r+1 ja -18000.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=22000-18000r^{2}-36000r-18000$$

Lahutage 18000 väärtusest 22000, et leida 4000.

$$IR^{2}r^{2}+2IR^{2}r+IR^{2}=4000-18000r^{2}-36000r$$

Kombineerige kõik liikmed, mis sisaldavad I.

$$\left(R^{2}r^{2}+2R^{2}r+R^{2}\right)I=4000-18000r^{2}-36000r$$

Võrrand on standardkujul.

$$\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I=4000-36000r-18000r^{2}$$

Jagage mõlemad pooled R^{2}r^{2}+2rR^{2}+R^{2}-ga.

$$\frac{\left(R^{2}r^{2}+2rR^{2}+R^{2}\right)I}{R^{2}r^{2}+2rR^{2}+R^{2}}=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}$$

R^{2}r^{2}+2rR^{2}+R^{2}-ga jagamine võtab R^{2}r^{2}+2rR^{2}+R^{2}-ga korrutamise tagasi.

$$I=\frac{4000-36000r-18000r^{2}}{R^{2}r^{2}+2rR^{2}+R^{2}}$$

Jagage 4000-18000r^{2}-36000r väärtusega R^{2}r^{2}+2rR^{2}+R^{2}.

$$I=\frac{2000\left(2-18r-9r^{2}\right)}{\left(R\left(r+1\right)\right)^{2}}$$

Lahendage ja leidke R (complex solution)

$$\left\{\begin{matrix}R=-\frac{20iI^{-\frac{1}{2}}\sqrt{45r^{2}+90r-10}}{r+1}\text{; }R=\frac{20iI^{-\frac{1}{2}}\sqrt{45r^{2}+90r-10}}{r+1}\text{, }&r\neq -1\text{ and }I\neq 0\\R\in \mathrm{C}\text{, }&\left(r=-\frac{\sqrt{11}}{3}-1\text{ or }r=\frac{\sqrt{11}}{3}-1\right)\text{ and }I=0\end{matrix}\right,$$