Question

if n+1=2010²+2011² then find the value of √2n+1

Answer 1

$n + 1 = 2010^2 + 2011^2 \\ \\ = n + 1 = 2010^2 + (2010 + 1)^2 \\ \\ = n + 1 = 2010^2 + 2010^2 + 2 \times 2010 + 1 \\ \\ \\ \therefore n = 2010^2 + 2010^2 + 2 \times 2010 \\ \\ = n = 2 \times 2010^2 + 2 \times 2010 \\ \\ \\ 2n = 2(2 \times 2010^2 + 2 \times 2010) \\ \\ = 2n = 4 \times 2010^2 + 4 \times 2010$

$\\ \\ \\ 2n + 1 = 4 \times 2010^2 + 4 \times 2010 + 1 \\ \\ = 2n + 1 = (2 \times 2010)^2 + (2 \times 2 \times 2010 \times 1) + 1^2 \\ \\ = 2n + 1 = ( 2 \times 2010 + 1)^2 \\ \\ \\ \sqrt{2n + 1} = \sqrt{(2 \times 2010 + 1)^2} \\ \\ = \sqrt{2n + 1} = 2 \times 2010 + 1 \\ \\ = \sqrt{2n + 1} = 4020 + 1 = 4021$

4021 is the answer.

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Answer 2

Answer:

4021

Step-by-step explanation:

I am saying short form

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