sqrt{a}=bsqrt{hk} を解きます| Microsoft 数学ソルバー

$$\sqrt { a } = b \sqrt { h k }$$

a を解く

$$a=hkb^{2}$$

$$\left(b\geq 0\text{ and }h\leq 0\text{ and }k\leq 0\right)\text{ or }\left(b\geq 0\text{ and }k\geq 0\text{ and }h\geq 0\right)\text{ or }h=0\text{ or }k=0$$

根号方程式を解くための手順

方程式の両辺を 2 乗します。

$$a=hkb^{2}$$

a を解く (複素数の解)

$$a=hkb^{2}$$

$$arg(b\sqrt{hk})<\pi \text{ or }k=0\text{ or }h=0\text{ or }b=0$$

b を解く (複素数の解)

$$\left\{\begin{matrix}b=\left(hk\right)^{-\frac{1}{2}}\sqrt{a}\text{, }&k\neq 0\text{ and }h\neq 0\\b\in \mathrm{C}\text{, }&\left(h=0\text{ or }k=0\right)\text{ and }a=0\end{matrix}\right.$$

b を解く

$$\left\{\begin{matrix}b=\sqrt{\frac{a}{hk}}\text{, }&\left(h<0\text{ and }k<0\text{ and }a\geq 0\right)\text{ or }\left(k>0\text{ and }h>0\text{ and }a\geq 0\right)\\b\in \mathrm{R}\text{, }&\left(h=0\text{ or }k=0\right)\text{ and }a=0\end{matrix}\right.$$