Let 2 ^2 x+3 x-2 0 and x^2-x-2 0 . ( x is measured in radians). The x lies in the interval

Step-by-step solution

2 ^2 x+3 x-2 0...(i) Let y= x Equation (i) becomes array ll & 2 y^2+3 y-2 0 & 2 y^2+4 y-y-2 0 & 2 y(y+2)-1(y+2) 0 & (2 y-1)(y+2) 0 & (2 y-1) 0 and (y+2) 0 OR & (2 y-1) 0 and (y+2) 0 array array ll & y 1 2 and y -2 & y 1 2 and y -2 & x 1 2 and x -2 & x 1 2 and x -2 array x 6 and x -2 [ -1 x 1 , second condition is not possible] x 6 and x -1 [ -1 x 1] aligned & x ( 6 , ) & Given that x^2-x-2 0 & (x-2)(x+1) 0 & (x-2) 0 and (x+1) 0 OR & (x-2) 0 and (x+1) 0 & x 2 and x -1 & x 2 and x -1 & x (-1,2) aligned OR ...(ii) [ s