Please explain this question Share with your friends Share 0 Gursheen Kaur answered this Dear Student, Solution) Given equation isx2-6x+x+7=0 ⇒x2-5x-x+x+7=0 ⇒x2-5x+7=x-x Nowx-x=x; where x denotes denotes fractional part of x and range of x is [0, 1) ⇒x2-5x+7=x The above equation can easily be solved graphically. Let gx=xand fx=x2-5x+7 which is an equation of vertical parabola So we have to solve fx=gx Consider ax2+bx+c=0Vertex of above equation is -b/2a, -b2-4ac/4a ⇒Vertex of fx= --5/2, -25-4×7×1/4= 2.5, 0.75f2=2×2-5×2+7= 1 and f3=3×3-5×3+7= 1Let us now draw the graph of fx and gx From above figure1 it is clear that fx and gx do not intersect each other which means fx is never equal to gx ; Note: x=0 when x is an integer .Hence g2=g3=0 whereas f2=f3=1 ⇒x2-5x+7=x will hold for no value of x Therefore the given equation x2-6x+x+7=0 has no solution. ⇒x∈∅ Regards​! 0 View Full Answer
