Question
Solve the following quadratic equations by factorization:$(a + b)^2 x^2 - 4abx - (a - b)^2 = 0$
✓
Answer
We have been given
$(a + b)^2 x^2 - 4abx - (a - b)^2 = 0$
$(a + b)^2 x^2 - (a + b)^2 x + - (a - b)^2 = 0$
$(a + b)^2 x(x - 1) + (a - b)^2 (x - 1) = 0$
$((a + b)^2 x + (a + b)^2) (x - 1) = 0$
Therefore,
$(a + b)^2 x + (a - b)^2 = 0$
$(a + b)^2 x = -(a - b)^2$^
$\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$
or, $x - 1 = 0$
$x = 1$
Hence, $\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$ or $x = 1$
$(a + b)^2 x^2 - 4abx - (a - b)^2 = 0$
$(a + b)^2 x^2 - (a + b)^2 x + - (a - b)^2 = 0$
$(a + b)^2 x(x - 1) + (a - b)^2 (x - 1) = 0$
$((a + b)^2 x + (a + b)^2) (x - 1) = 0$
Therefore,
$(a + b)^2 x + (a - b)^2 = 0$
$(a + b)^2 x = -(a - b)^2$^
$\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$
or, $x - 1 = 0$
$x = 1$
Hence, $\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$ or $x = 1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In figure, PQ || BC and AP : PB = 1 : 2. Find: $\frac{\text{area}(\triangle\text{APQ})}{\text{area}(\triangle\text{ABC})}$
→A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is $108\ cm$ and the diameter of the cylinder is $36\ cm$, find the cost of polishing the surface at the rate of $7$ paise per $cm^2$. $ (\text{Use}\ \pi=3.1416)$
→Solve the following quadratic equations by factorization:
$\frac{1}{\text{x}-1}-\frac{1}{\text{x}+5}=\frac{6}{7},$ $\text{x}\neq1,-5$
→$\frac{1}{\text{x}-1}-\frac{1}{\text{x}+5}=\frac{6}{7},$ $\text{x}\neq1,-5$
The $7^{\text {th }}$ term of an $A.P$. is $32$ and its $13^{\text {th }}$ term is $62$ . Find the $A.P.$
→Show that the following numbers are irrational.
$7\sqrt{5}$
→$7\sqrt{5}$
Two dice are thrown at the same time. Determine the probabiity that the difference of the numbers on the two dice is 2.
A wooden article was made by scooping out a hemisphere from each of the solid cylinder, as shown in fig. If the height of the cylinder is $10 \ cm$ and its base is of radius $3.5 \ cm .$ Find the total surface area of the article.
→Evaluate the following:
$ \frac{\tan^260^\circ+4\cos^245^\circ+3\sec^230^\circ+5\cos^290^\circ}{\text{cosec30}^\circ+\sec60^\circ-\cot^230^\circ}$
→$ \frac{\tan^260^\circ+4\cos^245^\circ+3\sec^230^\circ+5\cos^290^\circ}{\text{cosec30}^\circ+\sec60^\circ-\cot^230^\circ}$
Find the value of the middle term of the following $AP: -6,-2,2, \ldots ., 58$.
→A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.