已知\(m+1=2009^2+2010^2\),求\(\sqrt{2m+1}\)
设\(t=2009\),侧\(m+1=t^2+(t+1)^2\),
\(m+1=t^2+t^2+2t+1\)
\(m=2t^2+2t\)
原式\(\sqrt{2m+1}\)
=\(\sqrt{2(2t^2+2t)+1}\)
=\(\sqrt{4t^2+4t+1}\)
=\(\sqrt{(2t+1)^2}\)
=\(2t+1\)
\(t=2009\),求得\(\sqrt{2m+1}=2t+1=2 * 2009 +1=4019 \)