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Question

If x,y,z satisfies the equations
x+log(x+x2+1)=y
y+log(y+y2+1)=z
z+log(z+z2+1)=x, then find the value of (1x)2+(1y)2+(1z)2.

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Solution

If x , y , z satisfies the equations:
x+log(x+x2+1)=yy+log(y+y2+1)=zz+log(z+z2+1)=x
The equations are in cyclic form hence x = 0 , y = 0 , z = 0 ratifies equation and x = y = z satisfies these equations.
putting values of x , y , z in equation given:
(1x)2+(1y)2+(1z)2=(10)2+(10)2+(10)2=1+1+1=3
Ans = 3

1927428_185433_ans_ebecbe6ebb384fec9ad122fe0d6cb190.jpeg

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