Atrisiniet y=5pi^3/17-sqrt{2x}

$$y = \frac { 5 \pi ^ { 3 } } { 17 } - \sqrt { 2 x }$$

Atrast x

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$y\leq \frac{5\pi ^{3}}{17}$$

Vienādojumu sakņu atrisināšanas darbības

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

$$\frac{5\pi ^{3}}{17}-\sqrt{2x}=y$$

Atņemiet \frac{5\pi ^{3}}{17} no abām pusēm.

$$-\sqrt{2x}=y-\frac{5\pi ^{3}}{17}$$

Reiziniet vienādojuma abas puses ar 17.

$$-17\sqrt{2x}=17y-5\pi ^{3}$$

Daliet abas puses ar -17.

$$\frac{-17\sqrt{2x}}{-17}=\frac{17y-5\pi ^{3}}{-17}$$

Dalīšana ar -17 atsauc reizināšanu ar -17.

$$\sqrt{2x}=\frac{17y-5\pi ^{3}}{-17}$$

Daliet 17y-5\pi ^{3} ar -17.

$$\sqrt{2x}=-y+\frac{5\pi ^{3}}{17}$$

Kāpiniet kvadrātā abas vienādojuma puses.

$$2x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{289}$$

Daliet abas puses ar 2.

$$\frac{2x}{2}=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

Dalīšana ar 2 atsauc reizināšanu ar 2.

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

Daliet \frac{\left(-17y+5\pi ^{3}\right)^{2}}{289} ar 2.

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

Atrast x (complex solution)

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$arg(-\frac{y}{2}+\frac{5\pi ^{3}}{34})<\pi \text{ or }y=\frac{5\pi ^{3}}{17}$$

Atrast y (complex solution)

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

Atrast y

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

$$x\geq 0$$