Download App

Quadratic Equations — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
Solve the following quadratic equation:
$\frac{\text{a}}{(\text{ax}-\text{1})}+\frac{\text{b}}{(\text{bx}-\text{1})}=(\text{a}+\text{b}),$ $\text{x}\neq\frac{1}{\text{a}},\ \frac{1}{\text{b}}$
✓

Answer

$\frac{\text{a}}{(\text{ax}-\text{1})}+\frac{\text{b}}{(\text{bx}-\text{1})}=(\text{a}+\text{b})$
$\Rightarrow\Big[\frac{\text{a}}{\text{ax}-1}-\text{b}\Big]+\Big[\frac{\text{b}}{\text{bx}-1}-\text{a}\Big]=0$
$\Rightarrow\Big[\frac{\text{a}-\text{abx}+\text{b}}{\text{ax}-1}\Big]+\Big[\frac{\text{b}-\text{abx}+\text{a}}{\text{bx}-1}\Big]=0$
$\Rightarrow(\text{a}-\text{abx}+\text{b})\Big[\frac{1}{\text{ax}-1}+\frac{1}{\text{bx}-1}\Big]=0$
$\Rightarrow(\text{a}-\text{abx}+\text{b})$ or $\frac{1}{\text{ax}-1}+\frac{1}{\text{bx}-1}=0$
$\Rightarrow\text{abx}=\text{a}+\text{b}$ or $\frac{1}{\text{ax}-1}=-\frac{1}{\text{bx}-1}$
$\Rightarrow\text{x}=\frac{\text{a}+\text{b}}{\text{ab}}$ or $\text{bx} - 1 = -\text{ax} + 1$
$\Rightarrow\text{x}=\frac{\text{a}+\text{b}}{\text{ab}}$ or $\text{bx} + \text{ax} = 2$
$\Rightarrow\text{x}=\frac{\text{a}+\text{b}}{\text{ab}}$ or $\text{x}(\text{b} + \text{a}) = 2$
$\Rightarrow\text{x}=\frac{\text{a}+\text{b}}{\text{ab}}$ or $\text{x}=\frac{2}{\text{a}+\text{b}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Solve the following system of equations by the method of cross-multiplication:
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=13,$
$\frac{5}{\text{x}}-\frac{4}{\text{y}}=-2,$ where $\text{x}\neq0$ and $\text{y}\neq0.$
→
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$2\text{x}^2+5\sqrt3\text{x}+6=0$
→
In a circle of radius $21\ cm$, an arc subtends an angle of $60^\circ $ at the centre. Find
  1. The length of the arc.
  2. Area of the sector formed by the arc. $\Big(\text{Use }\pi=\frac{22}{7}\Big)$
→

If $3\cos\theta − 4 \sin \theta = 2 \cos \theta + \sin \theta$ find $\tan\theta.$

→
Point $A$ and $B$ are $70\ km$. a part on a highway. A car starts from $A$ and another car starts from $B$ simultaneously. If they travel in the same direction, they meet in $7$ hours, but if the travel towards each other, the meet in one hour. Find the speed of the two cars.
→
The cost of painting the four walls of a room $12\ m$ long at $₹ 30$ per $m^2$ is $₹ 7560$ and the cost of covering the floor with mat at $₹ 25$ per $m^2$ is $₹ 2700$. Find the dimensions of the room.
→
Solve the following systems of equations:
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=\frac{9}{\text{xy}},$
$\frac{4}{\text{x}}+\frac{9}{\text{y}}=\frac{21}{\text{xy}},\text{x}\neq0,\text{y}\neq0.$
→
Explain why $3 × 5 × 7 + 7$ is a composite number.
→
The rain water from a roof of $44\ m \times 20\ m$ drains into a cylindrical tank having diameter of base $4\ m$ and height $3.5\ m$. If the tank is just full, then find the rainfall in cm.
→
A well of diameter $2\ m$ is dug $14\ m$ deep. The earth taken out of it is spread evenly all around it to form an embankment of height $40\ cm$. Find the width of the embankment.
→