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# c3 easy question watch

1. 1 + x + (1+2x)lnx = o

find x
2. (Original post by nas7232)
1 + x + (1+2x)lnx = o

find x
You can't do it analytically so why not try a reduction formula?
lnx=-(1+x)/(1+2x)
x=e^[-(1+x)/(1+2x)]
3. (Original post by nas7232)
1 + x + (1+2x)lnx = o

find x
1 + x + lnx + 2xlnx = 0
lnx(1+2x) = -x-1
lnx = -(x+1)/(1+2x)
x = e-(x+1)/(1+2x)

Use the iteration formula;
xn+1 = e-(xn+1)/(1+2xn)

x1 = e-(0.5+1)/(1+1) = 0.47237.....
x2 = e-(0.47237+1)/(1+0.94473) = 0.46902.....
x3 = e-(0.46902+1)/(1+0.93804) = 0.46861.....
x4 = e-(0.46861+1)/(1+0.93721) = 0.46855.....
x5 = e-(0.46855+1)/(1+0.93711) = 0.46855.....

Therefore root of equation = 0.469 (3sf)

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