Expand the given expression (x+1 x )^6 - Vidyadip

Question

Expand the given expression $\left(x+\frac{1}{x}\right)^6$

✓

Answer

Using binomial theorem for the expansion of $\left(x+\frac{1}{x}\right)^6$
we have $\left(x+\frac{1}{x}\right)^6$
$={ }^6 C_0(x)^6+{ }^6 C_1(x)^5\left(\frac{1}{x}\right)+{ }^6 C_2(x)^4\left(\frac{1}{x}\right)^2+{ }^6 C_3(x)^3\left(\frac{1}{x}\right)^3+{ }^6 C_4(x)^2\left(\frac{1}{x}\right)^4+{ }^6 C_5(x)\left(\frac{1}{x}\right)^5+{ }^6 C_6\left(\frac{1}{6}\right)^6$
$=x^6+6 \cdot x^5 \cdot \frac{1}{x}+15 \cdot 4 x^4 \cdot \frac{1}{x^2}+20 \cdot x^3 \cdot \frac{1}{x^3}+15 \cdot x^2 \cdot \frac{1}{x^4}+6 \cdot x \cdot \frac{1}{x^5}+\frac{1}{x^6}$
$=x^6+6 x^4+15 x^2+20+\frac{15}{x^2}+\frac{6}{x^4}+\frac{1}{x^6}$

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 "3 Marks Question" from Model Paper 3→Model Paper 3 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Express $\frac { 5 + \sqrt { 2 } i } { 1 - \sqrt { 2 } i }$ in the form of a + ib.

Evaluate $\left[\frac{1}{1-4 i}-\frac{2}{1+i}\right]\left[\frac{3-4 i}{5+i}\right]$ to the standard form.

Find the mean deviation from the mean for the data:

$x_i$	$5$	$10$	$15$	$20$	$25$
$f_i$	$7$	$4$	$6$	$3$	$5$

How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?

Find the equation of the set of the point $P$, the sum of whose distance from $A(4, 0, 0)$ and $B(-4, 0, 0)$ is equal to $10.$

Find the coefficient of $x^4$ in the expansion of $(1 + x + x^2 + x^3 )^{11}.$

Shamshad Ali buys a scooter for $₹\ 22000.$ He pays $₹\ 4000$ cash and agrees to pay the balance in annual installment of $₹\ 1000$ plus $10\%$ interest on the unpaid amount. How much will the scooter cost him$?$

Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 0.

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

If P(n) is the statement "$n^2 - n + 41$ is prime", prove that $P(1), P(2)$ and $P(3)$ are true. Prove also that $P(41)$ is not true.