Issolvi -a=sqrt{2a^2+3ab-10}

$$-a = \sqrt{ 2 { a }^{ 2 } +3ab-10 }$$

Solvi għal b

$$b=-\frac{a}{3}+\frac{10}{3a}$$

$$a<0$$

Passi biex Issolvi l-Ekwazzjonijiet Radikali

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\sqrt{2a^{2}+3ab-10}=-a$$

Ikkwadra ż-żewġ naħat tal-ekwazzjoni.

$$3ab+2a^{2}-10=a^{2}$$

Naqqas 2a^{2}-10 miż-żewġ naħat tal-ekwazzjoni.

$$3ab+2a^{2}-10-\left(2a^{2}-10\right)=a^{2}-\left(2a^{2}-10\right)$$

Jekk tnaqqas 2a^{2}-10 minnu nnifsu jibqa' 0.

$$3ab=a^{2}-\left(2a^{2}-10\right)$$

Naqqas 2a^{2}-10 minn a^{2}.

$$3ab=10-a^{2}$$

Iddividi ż-żewġ naħat b'3a.

$$\frac{3ab}{3a}=\frac{10-a^{2}}{3a}$$

Meta tiddividi b'3a titneħħa l-multiplikazzjoni b'3a.

$$b=\frac{10-a^{2}}{3a}$$

Iddividi -a^{2}+10 b'3a.

$$b=-\frac{a}{3}+\frac{10}{3a}$$

Solvi għal a (complex solution)

$$\left\{\begin{matrix}a=\frac{-\sqrt{9b^{2}+40}-3b}{2}\text{, }&arg(\frac{-\sqrt{9b^{2}+40}-3b}{2})\geq \pi \\a=\frac{\sqrt{9b^{2}+40}-3b}{2}\text{, }&arg(\frac{\sqrt{9b^{2}+40}-3b}{2})\geq \pi \end{matrix}\right.$$

Solvi għal b (complex solution)

$$b=-\frac{a}{3}+\frac{10}{3a}$$

$$arg(a)\geq \pi \text{ and }a\neq 0$$

Solvi għal a

$$a=\frac{-\sqrt{9b^{2}+40}-3b}{2}$$

$$\left(\frac{\sqrt{9b^{2}+80}}{4}-\frac{\sqrt{9b^{2}+40}}{2}-\frac{3b}{4}\leq 0\text{ or }-\frac{\sqrt{9b^{2}+40}}{2}-\frac{\sqrt{9b^{2}+80}}{4}-\frac{3b}{4}\geq 0\right)\text{ and }b\leq \frac{\sqrt{9b^{2}+40}}{6}+\frac{3b}{2}$$