Let f (x) = x / e ^ 2x The number of roots of the equation | LNX | = f (x) about X is discussed

Let f (x) = x / e ^ 2x The number of roots of the equation | LNX | = f (x) about X is discussed

Now we know a function f (x) = LNX + x2-4x to find the number of roots of the equation f (x) + x2 = 0 on (1, + ∞)
Now we know a function f (x) = LNX + x2-4x
Finding the number of roots of the equation f (x) + x2 = 0 on (1, + ∞)

Let f (x) = LNX + x2-4x + X2, and get its derivative: F '(x) = 1 / x + 4x-4, because when x is (1, + ∞), f' (x) > 0, so f (x) is monotonically increasing, and f (x) is a continuous function, and f (1) = - 20, so there is only one point between (1,2), so that f (x) = 0, that is, LNX + x2-4x + x2 = 0, that is, f (x) + x2 = 0