Issolvi r=10*535134-2217*2489/sqrt{10*695135-(2489)^2-sqrt{10*607741-(2217)^2}}

$$r = \frac { 10 * 535134 - 2217 * 2489 } { \sqrt { 10 * 695135 - ( 2489 ) ^ { 2 } } - \sqrt { 10 * 607741 - ( 2217 ) ^ { 2 } } }$$

Solvi għal r

$$r = \frac{55591 {(\sqrt{756229} + \sqrt{1162321})}}{135364} \approx 799.887238416$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika 10 u 535134 biex tikseb 5351340.

$$r=\frac{5351340-2217\times 2489}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Immultiplika 2217 u 2489 biex tikseb 5518113.

$$r=\frac{5351340-5518113}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Naqqas 5518113 minn 5351340 biex tikseb -166773.

$$r=\frac{-166773}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Immultiplika 10 u 695135 biex tikseb 6951350.

$$r=\frac{-166773}{\sqrt{6951350-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Ikkalkula 2489 bil-power ta' 2 u tikseb 6195121.

$$r=\frac{-166773}{\sqrt{6951350-6195121}-\sqrt{10\times 607741-2217^{2}}}$$

Naqqas 6195121 minn 6951350 biex tikseb 756229.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{10\times 607741-2217^{2}}}$$

Immultiplika 10 u 607741 biex tikseb 6077410.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-2217^{2}}}$$

Ikkalkula 2217 bil-power ta' 2 u tikseb 4915089.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-4915089}}$$

Naqqas 4915089 minn 6077410 biex tikseb 1162321.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{1162321}}$$

Irrazzjonalizza d-denominatur tal-\frac{-166773}{\sqrt{756229}-\sqrt{1162321}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{756229}+\sqrt{1162321}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right)}$$

Ikkunsidra li \left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\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}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}\right)^{2}-\left(\sqrt{1162321}\right)^{2}}$$

Ikkwadra \sqrt{756229}. Ikkwadra \sqrt{1162321}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{756229-1162321}$$

Naqqas 1162321 minn 756229 biex tikseb -406092.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{-406092}$$

Iddividi -166773\left(\sqrt{756229}+\sqrt{1162321}\right) b'-406092 biex tikseb\frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right).

$$r=\frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{55591}{135364} b'\sqrt{756229}+\sqrt{1162321}.

$$r=\frac{55591}{135364}\sqrt{756229}+\frac{55591}{135364}\sqrt{1162321}$$

Assenja r

$$r≔\frac{55591\left(\sqrt{756229}+\sqrt{1162321}\right)}{135364}$$