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Quadratic Equations — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
Solve the following quadratoic equations by factorization:
$\frac{1}{2\text{a}+\text{b}+2\text{x}}=\frac{1}{2\text{a}}+\frac{1}{\text{b}}+\frac{1}{2\text{x}}$
✓

Answer

$\frac{1}{2\text{a}+\text{b}+2\text{x}}=\frac{1}{2\text{a}}+\frac{1}{\text{b}}+\frac{1}{2\text{x}}$$\Rightarrow\frac{1}{2\text{a}+\text{b}+2\text{x}}-\frac{1}{2\text{x}}=\frac{1}{2\text{a}}+\frac{1}{\text{b}}$
$\Rightarrow\frac{2\text{x}-(2\text{a}+\text{b}+2\text{x})}{(2\text{a}+\text{b}+2\text{x})2\text{x}}=\frac{\text{b}+2\text{a}}{2\text{ab}}$
$\Rightarrow\frac{-(2\text{a}+\text{b})}{(2\text{a}+\text{b}+2\text{x})2\text{x}}=\frac{(2\text{a}+\text{b})}{2\text{ab}}$
$\Rightarrow(2\text{a}+\text{b}+2\text{x})2\text{x}=-2\text{ab}$
$\Rightarrow4\text{ax}+2\text{bx}+4\text{x}^2+2\text{ab}=0$
$\Rightarrow4\text{x}^2+4\text{ax}+2\text{bx}+2\text{ab}=0$ (Dividing by 2)
$\Rightarrow2\text{x}^2+2\text{ax}+\text{bx}+\text{ab}=0$
$\Rightarrow2\text{x}(\text{x}+\text{a})+\text{b}(\text{x}+\text{a})=0$
$\Rightarrow(\text{x}+\text{a})(2\text{x}+\text{b})=0$
Either $\text{x}+\text{a}=0$ or $2\text{x}+\text{b}=0$
$\Rightarrow\text{x}=-\text{a}$ or $\text{x}=\frac{-\text{b}}{2}$

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