Lahenda HB=1500/314*5*(5-sqrt{5^2-2295^2)}

$$H B = \frac { 1500 } { 314 \cdot 5 \cdot ( 5 - \sqrt { 5 ^ { 2 } - 2295 ^ { 2 } } ) }$$

Lahendage ja leidke B

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

$$H\neq 0$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage 5 ja 314, et leida 1570.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

Arvutage 2 aste 5 ja leidke 25.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

Arvutage 2 aste 2295 ja leidke 5267025.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

Lahutage 5267025 väärtusest 25, et leida -5267000.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Tegurda -5267000=\left(10i\right)^{2}\times 52670. Kirjutage \sqrt{\left(10i\right)^{2}\times 52670} toote juured, kui see ruut \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Leidke \left(10i\right)^{2} ruutjuur.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

Kasutage distributiivsusomadust, et korrutada 1570 ja 5-10i\sqrt{52670}.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

Ratsionaliseerige korrutades lugeja ja 7850+15700i\sqrt{52670} nimetaja \frac{1500}{7850-15700i\sqrt{52670}} nimetaja.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Mõelge valemile \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

Arvutage 2 aste 7850 ja leidke 61622500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

Laiendage \left(-15700i\sqrt{52670}\right)^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

Arvutage 2 aste -15700i ja leidke -246490000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

\sqrt{52670} ruut on 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

Korrutage -246490000 ja 52670, et leida -12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

Korrutage -1 ja -12982628300000, et leida 12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

Liitke 61622500 ja 12982628300000, et leida 12982689922500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

Jagage 1500\left(7850+15700i\sqrt{52670}\right) väärtusega 12982689922500, et leida \frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

Kasutage distributiivsusomadust, et korrutada \frac{1}{8655126615} ja 7850+15700i\sqrt{52670}.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Muutke liikmete järjestust.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

Võrrand on standardkujul.

$$HB=\frac{10+20\sqrt{52670}i}{11025639}$$

Jagage mõlemad pooled H-ga.

$$\frac{HB}{H}=\frac{10+20\sqrt{52670}i}{11025639H}$$

H-ga jagamine võtab H-ga korrutamise tagasi.

$$B=\frac{10+20\sqrt{52670}i}{11025639H}$$

Jagage \frac{10+20i\sqrt{52670}}{11025639} väärtusega H.

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

Lahendage ja leidke H

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$

$$B\neq 0$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage 5 ja 314, et leida 1570.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

Arvutage 2 aste 5 ja leidke 25.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

Arvutage 2 aste 2295 ja leidke 5267025.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

Lahutage 5267025 väärtusest 25, et leida -5267000.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Tegurda -5267000=\left(10i\right)^{2}\times 52670. Kirjutage \sqrt{\left(10i\right)^{2}\times 52670} toote juured, kui see ruut \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Leidke \left(10i\right)^{2} ruutjuur.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

Kasutage distributiivsusomadust, et korrutada 1570 ja 5-10i\sqrt{52670}.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

Ratsionaliseerige korrutades lugeja ja 7850+15700i\sqrt{52670} nimetaja \frac{1500}{7850-15700i\sqrt{52670}} nimetaja.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Mõelge valemile \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

Arvutage 2 aste 7850 ja leidke 61622500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

Laiendage \left(-15700i\sqrt{52670}\right)^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

Arvutage 2 aste -15700i ja leidke -246490000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

\sqrt{52670} ruut on 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

Korrutage -246490000 ja 52670, et leida -12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

Korrutage -1 ja -12982628300000, et leida 12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

Liitke 61622500 ja 12982628300000, et leida 12982689922500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

Jagage 1500\left(7850+15700i\sqrt{52670}\right) väärtusega 12982689922500, et leida \frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

Kasutage distributiivsusomadust, et korrutada \frac{1}{8655126615} ja 7850+15700i\sqrt{52670}.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Muutke liikmete järjestust.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

Võrrand on standardkujul.

$$BH=\frac{10+20\sqrt{52670}i}{11025639}$$

Jagage mõlemad pooled B-ga.

$$\frac{BH}{B}=\frac{10+20\sqrt{52670}i}{11025639B}$$

B-ga jagamine võtab B-ga korrutamise tagasi.

$$H=\frac{10+20\sqrt{52670}i}{11025639B}$$

Jagage \frac{10+20i\sqrt{52670}}{11025639} väärtusega B.

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$