How to prove that g(x) =(ln2) cos (pi.x) /2 +1/x has a root lying between 1 and 2 by applying a mean value theorem to f(x) =(ln2) sin (pi.x) /2 +logx -
![If x,y,z satisfies the equations x + log ( x + √(x^2+1)) = y y + log ( y + √(y^2+1)) = z z + log ( z + √(z^2+1)) = x , then find the value of ( 1 - x )^2 + ( 1 - y )^2 + ( 1 - z )^2 . If x,y,z satisfies the equations x + log ( x + √(x^2+1)) = y y + log ( y + √(y^2+1)) = z z + log ( z + √(z^2+1)) = x , then find the value of ( 1 - x )^2 + ( 1 - y )^2 + ( 1 - z )^2 .](https://dwes9vv9u0550.cloudfront.net/images/1788913/bd1ac658-5acb-4d6f-9887-8985a6e9e73e.jpg)
If x,y,z satisfies the equations x + log ( x + √(x^2+1)) = y y + log ( y + √(y^2+1)) = z z + log ( z + √(z^2+1)) = x , then find the value of ( 1 - x )^2 + ( 1 - y )^2 + ( 1 - z )^2 .
![Show that `y=a cos(log x)+b sin(log x)` is a solution of the differential equation `x^2(d^2y)/... - YouTube Show that `y=a cos(log x)+b sin(log x)` is a solution of the differential equation `x^2(d^2y)/... - YouTube](https://i.ytimg.com/vi/ZtmdV6bD-b8/maxresdefault.jpg)