Let the point be P(x, y). Since it lies on the x-axis ∴ y = 0 i.e., required point be (x, 0). Since the required point is equidistant from points A(7, 6) and B(3, 4) ⇒ PA = PB ⇒ $\sqrt{(x-7)^2+(0-6)^2}$ = $\sqrt{(x-3)^2+(0-4)^2}$ ⇒ $\sqrt{x^2+49-14x+36}$ = $\sqrt{x^2+9-6x+16}$ ⇒ $x^2$ - 14x + 85 = $x^2$ - 6x + 25 ⇒ - 14x + 6x = 25 - 85 ⇒ 8x = 60 ⇒ x = $\frac{15}{2}$ ∴ The required point is $\left(\frac{15}{2},0\right)$