Step 1: The given equation is \(2x^5 + 5x = 3x^3 + 4x^4\). To solve it, first move all terms to one side:
\[ 2x^5 + 5x - 3x^3 - 4x^4 = 0 \]
Step 2: Factor the equation:
\[ x(2x^4 + 5 - 3x^2 - 4x^3) = 0 \]
This gives one solution \(x = 0\).
Step 3: For the remaining equation \(2x^4 - 4x^3 - 3x^2 + 5 = 0\), numerically solving it or using graphing tools, we find that the equation has only one non-zero real solution.
Step 4: Therefore, the equation has only one non-zero real solution.
A uniform rod AB of length 1 m and mass 4 kg is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the rod A and Bare 3 m/s and 4 m/s respectively, as shown in the figure. Then which of the following statement(s) is/are correct?