Question

Find the number of positive integers'n' , such that√n+√n+1<11.

Answer 1

Step-by-step explanation:

We have,

$\sqrt{n} + \sqrt{n + 1} < 11$

$\implies \sqrt{n} < 11 - \sqrt{n + 1}$

$\implies \: n < 122+ n - 22 \sqrt{n + 1}$

$\implies22 \sqrt{n + 1} < 122$

$\implies \sqrt{n + 1} < \frac{122}{22}$

$\implies \sqrt{n + 1} < \frac{61}{11}$

$\implies(n + 1) < \frac{3721}{121}$

$\implies \: n < \frac{3721 - 121}{121}$

$\implies \: n < \frac{3600}{121}$

$\implies \: n < 29.75$

Hence, 29 positive integers are satisfying the given condition