Question
Evaluate the following:
$(3+\sqrt2)^5-(3-\sqrt2)^5$
Evaluate the following:
$(3+\sqrt2)^5-(3-\sqrt2)^5$
$(3+\sqrt2)^5-(3-\sqrt2)^5$
$=2\big[{^5\text{C}}_1(3)^4(\sqrt2)^1+{^5\text{C}}_3(3)^2(\sqrt2)^3+{^5\text{C}}_5(\sqrt3)^5\big]$
$=2\big[5\times81\times\sqrt2+10\times9\times2\sqrt2+4\sqrt2\big]$
$=2\big[405\sqrt2+180\sqrt2+4\sqrt2\big]$
$=2\big[589\sqrt2\big]$
$=1178\sqrt2$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| Age (on nearest birth day) | 17-19.5 | 20-25.5 | 26-35.5 | 36-40.5 | 41-50.5 | 51-55.5 | 56-60.5 | 61-70.5 |
| No. of persons | 5 | 16 | 12 | 26 | 14 | 12 | 6 | 5 |
Find the term independent of x in the expansion of the following expressions:
$\Big(\frac{1}{2}\text{x}^{\frac{1}{3}}+\text{x}^{-\frac{1}{5}}\Big)^{8}$
Prove that the coefficient of (r + 1)th term in the expansion of $(1+\text{x})^{\text{n+1}}$ is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of $(1+\text{x})^{\text{n}}.$