The number of all values of in the interval (- 2 , 2 ) satisfying the equation (1- )(1+ ) ^2 +2 ^2 =0 is

Step-by-step solution

aligned & (1- )(1+ ) ^2 +2 ^2 =0 & (1- ^2 ) (1+ ^2 )+2 ^2 =0 aligned Put ^2 =x aligned & (1-x)(1+x)+2 x=0 & 1-x^2+2 x=0 & x^2-1=2 x aligned Let us draw graph of y=x^2-1 and y=2 x From the graph the two curves are intersecting at 2 points. There are 2 values of x . Only one value of x exists, for ( - 2 , 2 ) x= ^2 Two values of satisfies above equation