Find the number of irrational solutions of the equation x^2+ x^2+11 + x^2- x^2+11 =4

Step-by-step solution

Put x^2+11 =1 so that x^2+ x^2+11 + x^2- x^2+11 =4 can be written as t^2+1-11 + t^2-1-11 We have also have the identity (t^2+t-11 )- (t^2-t-11 )=2 t ...(2) Dividing (1) by (2), we get t^2+t-11 - t^2-1-11 = t 2 ...(3) Adding (2) and (3), we get aligned & 2 ( t^2+t-11 )=4+ t 2 & t^2+t-11=4+t+ t^2 16 t=4 x= 5 aligned