The equation |1-x|+x^2=5 has

Step-by-step solution

aligned & |1-x|+x^2=5 & |x-1|+x^2=5 aligned First case: If x 1,|x-1| is negative. aligned & -( x -1)+ x ^2=5 & - x +1+ x ^2=5 & x ^2- x +1=5 & x ^2- x -4=0 & Roots are -(-1) (-1)^2-4(1)(-4) 2(1) aligned = 1 1+16 2 = 1 17 2 Since, x 1 , root cannot be 1+ 17 2 . So, the root is 1- 17 2 , which is irrational. Second case: If x 1,|x-1|=x-1 array ll & | x -1|+ x ^2=5 & x -1+ x ^2=5 & x ^2+ x -6=0 & x ^2+3 x -2 x -6=0 & x ( x +3)-2( x +3)=0 & x =2,-3 array Since x 1 , root cannot be -3 . So, root is 2 which is rational.