Which of the following value of satisfy
$x = 1 + \frac{1}{x + \frac{1}{x + \frac{1}{x + . . . . . . .}}}$

Question

Which of the following value of satisfy
x = 1 + 1 x + 1 x + 1 x +

Brijendra Pal · Accepted Answer

Hi, x = 1+1x+1x+1x+
add x-1 both side,2x -1  = x+1x+1x+1x+
now the pattern will repeat as shown in the box, 2x -1  = x+1x+1x+1x+
2x -1  = x+12x-12x -12= x2x-1+14x2+1-4x=2x2-x+12x2-3x =0 x2x-3= 0 x = 0 or 32but x cannot be 0 as it does not satisfy original equation so x = 32

Which of the following value of satisfy x = 1 + 1 x + 1 x + 1 x + . . . . . . .

Which of the following value of satisfy
$x = 1 + \frac{1}{x + \frac{1}{x + \frac{1}{x + . . . . . . .}}}$