Question
If $\left(x+\frac{1}{x}\right)^2=3$, show that $\left(x^3+\frac{1}{x^3}\right)=0$.
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Answer
self
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The marks obtained by 40 students of a class in an examination are given below.
Present the data in the form of a frequency distribution using equal class-size, one such class being 10 - 15 (15 not included).
3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 21, 6, 23, 15
Present the data in the form of a frequency distribution using equal class-size, one such class being 10 - 15 (15 not included).
3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 21, 6, 23, 15
The length and breadth of a rectangular field are in the ratio $8: 5. A 2\ m$ wide path runs all around outside the field. The area of the path is $848\ m^2$. Find the length and breadth of the field.
→The following figure shows a circle with center $O$.
If $O P$ is perpendicular to $A B$, prove that $A P=B P$.
→If $O P$ is perpendicular to $A B$, prove that $A P=B P$.
In the given figure, $A B C D$ is a parallelogram. Side $D C$ is produced to E and $\angle BCE =105^{\circ}$.
Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
→Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
Two cubes, each of volume $512 cm ^3$ are joined end to end. Find the surface area of the resulting cuboid.
→The graph of $3x + 2y = 6$ meets the $x-$axis at point $P$ and the $y-$axis at point $Q.$ Use the graphical method to find the co$-$ordinates of points $P$ and $Q$.
→Find the amount and the compound interest on the following :$Rs.15000$ for $2$ years at $8\%$ per annum compounded semi$-$annually.
→Simplify using suitable identity:
(3x - 5y - 4) (9x2 + 25y2 + 16 +15xy - 20y + 12x)
(3x - 5y - 4) (9x2 + 25y2 + 16 +15xy - 20y + 12x)
Prove that:
$\left(\frac{x^a}{x^b}\right)^{(a+b-c)} \cdot\left(\frac{x^b}{x^c}\right)^{(b+c-a)} \cdot\left(\frac{x^c}{x^a}\right)^{c+a-b}=1$.
→$\left(\frac{x^a}{x^b}\right)^{(a+b-c)} \cdot\left(\frac{x^b}{x^c}\right)^{(b+c-a)} \cdot\left(\frac{x^c}{x^a}\right)^{c+a-b}=1$.
In the given figure, $A P$ is the bisector of $\angle A$ and $C Q$ is the bisector of $\angle C$ of parallelogram $\text{ABCD}$.
Prove that $\text{APCQ}$ is a parallelogram.
→Prove that $\text{APCQ}$ is a parallelogram.