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# 用平方根求解二次方程

#### 本课内容

${x}^{2}=36$
$\left(x-2{\right)}^{2}=49$
$2{x}^{2}+3=131$

## 解答${x}^{2}=36$‍ 以及类似的方程

$\begin{array}{rl}{x}^{2}& =36\\ \\ \sqrt{{x}^{2}}& =\sqrt{36}& & \text{取平方根.}\\ \\ x& =±\sqrt{36}\\ \\ x& =±6\end{array}$

### $±$‍ 号是什么意思

$±$号是一种能更迅速表达这种概念的符号.例如$±6$表示”$6$$-6$“.

### 有关逆运算的要点

${x}^{2}=16$.
$x=±$

${x}^{2}=81$.
$x=±$

${x}^{2}=5$.

## 解答$\left(x-2{\right)}^{2}=49$‍ 以及类似的方程

$\begin{array}{rl}\left(x-2{\right)}^{2}& =49\\ \\ \sqrt{\left(x-2{\right)}^{2}}& =\sqrt{49}& & \text{取平方根.}\\ \\ x-2& =±7\\ \\ x& =±7+2& & \text{加2.}\end{array}$

### 看懂解法

$\left(x+3{\right)}^{2}=25$.

$\left(2x-1{\right)}^{2}=9$.

$\left(x-5{\right)}^{2}=7$.

### 为什么不该展开括号

${x}^{2}-4x+4=49$

## 解答$2{x}^{2}+3=131$‍ 类型的一元二次方程

$\begin{array}{rl}2{x}^{2}+3& =131\\ \\ 2{x}^{2}& =128& & \text{减去3.}\\ \\ {x}^{2}& =64& & \text{除以2.}\\ \\ \sqrt{{x}^{2}}& =\sqrt{64}& & \text{取平方根.}\\ \\ x& =±8\end{array}$

$3{x}^{2}-7=5$.

$4\left(x-1{\right)}^{2}+2=38$.

${x}^{2}+8x+16=9$.