If x ( +y)= y and y= m x^2+2 n x+1 then m^2=

Step-by-step solution

aligned & Given, x ( +y)= y and y= m x^2+2 n x+1 & x ( +y)= y & ( +y) y = 1 x & y+ y y = 1 x & y+ = 1 x & y= 1-x x & y= x 1-x & y= ⁻¹ [ x 1-x ] & .y^ = 1 1+ ( x 1-x )^2 ] & . y^ = [(1-x ) -x (- ) (1-x )^2 ] & [ -x )^2+(x )^2 (1-x )^2 . aligned aligned & y^ = 1+x^2 ^2 -2 x +x^2 ^2 & y^ = x^2-2 x +1 aligned Here, m= and n=- aligned m^2 & = ^2 & =1- ^2 =1-n^2 aligned