Evaluate the following: (2+ 3)^7+(2- 3)^7 - Vidyadip

Question

Evaluate the following:

$(2+\sqrt3)^7+(2-\sqrt3)^7$

✓

Answer

$(2+\sqrt3)^7+(2-\sqrt3)^7$

$=2\Big[{^7\text{C}}_02^7+{^7\text{C}}_2{2}^5(\sqrt3)^2+{^7\text{C}}_4(2)^4(\sqrt3)^4+{^7\text{C}}_6{2}(\sqrt{3})^6\Big]$

$=2\Big[128+21\times32\times3+35\times8\times9+7\times2\times27\Big]$

$=2\big[128+2016+2520+378\big]$

$=2\big[5042\big]$

$=10084$

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 Binomial Theorem→Binomial Theorem — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A man saved ₹ 16,500 in ten years. In each year after the first he saved ₹ 100 more than he did in the receding year. How much did he save in the first year?

Solve the following linear inequations in R:
$\frac{7\text{x}-5}{8\text{x}+3}>4$

A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\tan\text{x}}{1-\cos\text{x}}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$

Find the mean deviation about the mean for the data

Height in cm	95-105	105-115	115-125	125-135	135-145	145-155
Number of boys	9	13	26	30	12	10

Find the domain and range of the following real valued functions:
f(x) = |x - 1|

Prove that:
$\tan225^\circ\cot405^\circ+\tan765^\circ\cot675^\circ=0$

If $\sin\text{x}=\frac{3}{5},\tan\text{y}=\frac{1}{2}$ and $\frac{\pi}{2}<\text{x}<\pi<\text{y}<\frac{3\pi}{2},$ find the value of $8\tan\text{x}-\sqrt{5}\sec\text{y}.$