Question
Solve the following quadratic equations by factorization:
$\text{x}-\frac{1}{\text{x}}=3,\text{x}\neq0$
$\text{x}-\frac{1}{\text{x}}=3,\text{x}\neq0$
✓
Answer
$\text{x}-\frac{1}{\text{x}}=3$
$\Rightarrow\text{x}^2-3\text{x}-1=0$
Here $\text{a}=1,\text{b}=-3,\text{c}=-1$
$\therefore\text{D}=\text{b}^2-4\text{ac}$
$=(-3)^2-4\times(1)(-1)$
$=9+4=13$
$\therefore\text{x} = {-\text{b} \pm \sqrt{\text{b}^2-4\text{ac}} \over 2\text{a}}$
$\text{x}={-(-3) \pm \sqrt{13} \over 2\times1}$
$\text{x}=\frac{3\pm\sqrt{13}}{2}$
$\Rightarrow\text{x}^2-3\text{x}-1=0$
Here $\text{a}=1,\text{b}=-3,\text{c}=-1$
$\therefore\text{D}=\text{b}^2-4\text{ac}$
$=(-3)^2-4\times(1)(-1)$
$=9+4=13$
$\therefore\text{x} = {-\text{b} \pm \sqrt{\text{b}^2-4\text{ac}} \over 2\text{a}}$
$\text{x}={-(-3) \pm \sqrt{13} \over 2\times1}$
$\text{x}=\frac{3\pm\sqrt{13}}{2}$
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
If $\cos\text{A}=\frac{7}{25},$ find is the value of $\tan\text{A}+\cot\text{A}$.
→In $\triangle O P Q$ right angled at $P, OP = 7\ cm, OQ - PQ = 1\ cm.$ Determine the values of $\sin Q$ and $\cos Q.$
→A box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
→- red $?$
- white $?$
- not green $?$
For what value of $k,$ is $3$ a zero of the polynomial $2x^2+ x + k?$
→Half the perimeter of a garden, whose length is $4$ more than its width is $36\ m.$ Find the dimension of the garden.
→$AB$ is a chord of a circle with centre $O$ and radius $4\ cm. AB$ is of length $4\ cm$ and divides the circle into two segments. Find the area of the minor segment.
→Prove the following trigonometric identities.
$(1+\cot\text{A}-\text{cosec A})(1+\tan\text{A}+\sec\text{A})=2$
→$(1+\cot\text{A}-\text{cosec A})(1+\tan\text{A}+\sec\text{A})=2$
Sides $AB$ and $BC$ and median $AD$ of a triangle $ABC$ are respectively proportional to sides $PQ$ and $QR$ and median $PM$ of $\triangle PQR ($see figure$).$ Show that $\triangle A B C \sim \triangle P Q R$
→A circular pond is of diameter $17.5\ m.$ It is surrounded by a $2\ m$ wide path. Find the cost of constructing the path at the rate of $₹\ 25$ per square metre. $(\text{Use }\pi=3.14)$
→In the given figure, there are two concentric circles with centre $O$ of radii 5cm and 3cm. From an external point $P,$ tangent $PA$ and $PB$ are drawn to these circles.
If $AP = 12\ cm,$ find the length of $BP.$
→If $AP = 12\ cm,$ find the length of $BP.$