1x-2x+3x-....2010x+2011x=2012
x(1-2+3-4....-2010+2011)=2012
x(-1×2010/2+2011)=2012
x(-1005+2011)=2012
1006x=2012
x=2
√3(√2x+1)+√2(√3x+1)=2x × √(7+2√6) - √(5-2√6)
√(7+2√6) =√(7+√24)=√(7+5)/2+√(7-5)/2=√6+1
a=7
b=24
√(a²-b)=√(7²-24)=√(49-24)=√25=5
√(a+√b)=√{[a+√(a²-b)]/2}+√{[a-√(a²-b)]/2}=√(7+5)/2+√(7-5)/2=√6+1
√(5-2√6)=√(5-√24) =√(5+1)/2-√(5-1)/2=√3-√2
a=5
b=24
√(a²-b)=√(5²-24)=√(25-24)=√1=1
√3(√2x+1)+√2(√3x+1)=2x × √(7+2√6) - √(5-2√6)
x√6+√3+x√6+√2=2x ×(√6+1)-√3+√2
2x√6+√3+√2=2x√6+2x-√3+√2
+√3=+2x-√3
2x=2√3
x=√3
