Let f(x) = -3 + x - x2 Then, f(x) < 0 for all x because coefficient of x2 < 0 and disc < 0. Thus, LHS of the given equation is always positive whereas the RHS is always less than zero. Hence, the given equation has no solution. Alternate Solution: Given, equation is
9
10
= - 3 + x - x2
Let y =
9
10
, therefore y = - 3 + x - x2 y = [x2−x+
1
4
] - 3 +
1
4
⇒ y =
11
4
= - (x−
1
2
)2 It is clear from the graph that two curves do not intersect. Hence, no solution exists