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

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

Solvi għal B

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

$$H\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika 5 u 314 biex tikseb 1570.

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

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

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

Ikkalkula 2295 bil-power ta' 2 u tikseb 5267025.

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

Naqqas 5267025 minn 25 biex tikseb -5267000.

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

Iffattura -5267000=\left(10i\right)^{2}\times 52670. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{\left(10i\right)^{2}\times 52670} bħala l-prodott tal-għeruq kwadrati \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Ħu l-għerq kwadrat ta' \left(10i\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 1570 b'5-10i\sqrt{52670}.

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

Irrazzjonalizza d-denominatur tal-\frac{1500}{7850-15700i\sqrt{52670}} billi timmultiplika in-numeratur u d-denominatur mill-7850+15700i\sqrt{52670}.

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

Ikkunsidra li \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkalkula 7850 bil-power ta' 2 u tikseb 61622500.

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

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

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

Ikkalkula -15700i bil-power ta' 2 u tikseb -246490000.

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

Il-kwadrat ta' \sqrt{52670} huwa 52670.

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

Immultiplika -246490000 u 52670 biex tikseb -12982628300000.

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

Immultiplika -1 u -12982628300000 biex tikseb 12982628300000.

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

Żid 61622500 u 12982628300000 biex tikseb 12982689922500.

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

Iddividi 1500\left(7850+15700i\sqrt{52670}\right) b'12982689922500 biex tikseb\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

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

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{8655126615} b'7850+15700i\sqrt{52670}.

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

Erġa' ordna t-termini.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'H.

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

Meta tiddividi b'H titneħħa l-multiplikazzjoni b'H.

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

Iddividi \frac{10+20i\sqrt{52670}}{11025639} b'H.

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

Solvi għal H

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

$$B\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika 5 u 314 biex tikseb 1570.

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

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

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

Ikkalkula 2295 bil-power ta' 2 u tikseb 5267025.

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

Naqqas 5267025 minn 25 biex tikseb -5267000.

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

Iffattura -5267000=\left(10i\right)^{2}\times 52670. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{\left(10i\right)^{2}\times 52670} bħala l-prodott tal-għeruq kwadrati \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Ħu l-għerq kwadrat ta' \left(10i\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 1570 b'5-10i\sqrt{52670}.

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

Irrazzjonalizza d-denominatur tal-\frac{1500}{7850-15700i\sqrt{52670}} billi timmultiplika in-numeratur u d-denominatur mill-7850+15700i\sqrt{52670}.

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

Ikkunsidra li \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkalkula 7850 bil-power ta' 2 u tikseb 61622500.

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

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

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

Ikkalkula -15700i bil-power ta' 2 u tikseb -246490000.

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

Il-kwadrat ta' \sqrt{52670} huwa 52670.

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

Immultiplika -246490000 u 52670 biex tikseb -12982628300000.

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

Immultiplika -1 u -12982628300000 biex tikseb 12982628300000.

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

Żid 61622500 u 12982628300000 biex tikseb 12982689922500.

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

Iddividi 1500\left(7850+15700i\sqrt{52670}\right) b'12982689922500 biex tikseb\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

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

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{8655126615} b'7850+15700i\sqrt{52670}.

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

Erġa' ordna t-termini.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'B.

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

Meta tiddividi b'B titneħħa l-multiplikazzjoni b'B.

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

Iddividi \frac{10+20i\sqrt{52670}}{11025639} b'B.

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