MCQ
If $(x+1)(2 x+8)=(x+7)(x+3)$, then using factorisation method, the values of $x$ are:
- A$\sqrt{12}, \sqrt{13}$
- B$-\sqrt{13},-\sqrt{13}$
- ✓$\pm \sqrt{13}$
- D$\sqrt{13}, \sqrt{13}$
✓
Answer
Correct option: C.
$\pm \sqrt{13}$
(c) $\pm \sqrt{13}$
Explanation:
We have,
$\begin{array}{l}(x+1)(2 x+8)=(x+7)(x+3) \\ \Rightarrow 2 x^2+10 x+8=x^2+10 x+21 \\ \Rightarrow x^2-13=0 \\ \Rightarrow(x)^2-(\sqrt{13})^2=0 \\ \Rightarrow(x-\sqrt{13})(x+\sqrt{13})=0 \\ \Rightarrow x=-\sqrt{13}, \sqrt{13} .\end{array}$
Explanation:
We have,
$\begin{array}{l}(x+1)(2 x+8)=(x+7)(x+3) \\ \Rightarrow 2 x^2+10 x+8=x^2+10 x+21 \\ \Rightarrow x^2-13=0 \\ \Rightarrow(x)^2-(\sqrt{13})^2=0 \\ \Rightarrow(x-\sqrt{13})(x+\sqrt{13})=0 \\ \Rightarrow x=-\sqrt{13}, \sqrt{13} .\end{array}$
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