Lutasin ang {l}{x+y+z=15quad1/61quadsqrt{y}quadxy+yz+xz=45}{sqrt{a}quadx^2+y^2+z^2=?}

$$\left. \begin{array} { l } { x + y + z = 15 \quad \frac { 1 } { 61 } \quad \sqrt { y } \quad x y + y z + x z = 45 } \\ { \sqrt { a } \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = ? } \end{array} \right.$$

I-solve ang x

$$\left\{\begin{matrix}x=-\frac{61\left(z+y-yz\right)}{61-61z-916y^{\frac{3}{2}}}\text{, }&\left(\frac{61-61z}{916}<0\text{ or }y\neq \frac{\left(6397802-6397802z\right)^{\frac{2}{3}}}{209764}\right)\text{ and }y\geq 0\\x\in \mathrm{R}\text{, }&\frac{61-61z}{916}\geq 0\text{ and }\left(z\leq 0\text{ or }z>1\right)\text{ and }y=-\frac{z}{1-z}\text{ and }-\frac{z}{1-z}=\frac{\left(6397802-6397802z\right)^{\frac{2}{3}}}{209764}\end{matrix}\right.$$

Mga Hakbang sa Pagso-solve ng Linear Equation

I-multiply ang magkabilang dulo ng equation gamit ang 61.

$$61x+61y+61z=\left(15\times 61+1\right)\sqrt{y}xy+61yz+61xz$$

I-multiply ang 15 at 61 para makuha ang 915.

$$61x+61y+61z=\left(915+1\right)\sqrt{y}xy+61yz+61xz$$

Idagdag ang 915 at 1 para makuha ang 916.

$$61x+61y+61z=916\sqrt{y}xy+61yz+61xz$$

I-subtract ang 916\sqrt{y}xy mula sa magkabilang dulo.

$$61x+61y+61z-916\sqrt{y}xy=61yz+61xz$$

I-subtract ang 61xz mula sa magkabilang dulo.

$$61x+61y+61z-916\sqrt{y}xy-61xz=61yz$$

I-subtract ang 61y mula sa magkabilang dulo.

$$61x+61z-916\sqrt{y}xy-61xz=61yz-61y$$

I-subtract ang 61z mula sa magkabilang dulo.

$$61x-916\sqrt{y}xy-61xz=61yz-61y-61z$$

Pagsamahin ang lahat ng term na naglalaman ng x.

$$\left(61-916\sqrt{y}y-61z\right)x=61yz-61y-61z$$

Ang equation ay nasa standard form.

$$\left(-916\sqrt{y}y-61z+61\right)x=61yz-61y-61z$$

I-divide ang magkabilang dulo ng equation gamit ang 61-916\sqrt{y}y-61z.

$$\frac{\left(-916\sqrt{y}y-61z+61\right)x}{-916\sqrt{y}y-61z+61}=\frac{61yz-61y-61z}{-916\sqrt{y}y-61z+61}$$

Kapag na-divide gamit ang 61-916\sqrt{y}y-61z, ma-a-undo ang multiplication gamit ang 61-916\sqrt{y}y-61z.

$$x=\frac{61yz-61y-61z}{-916\sqrt{y}y-61z+61}$$

I-divide ang 61yz-61y-61z gamit ang 61-916\sqrt{y}y-61z.

$$x=\frac{61\left(yz-y-z\right)}{61-61z-916y^{\frac{3}{2}}}$$