Find the smallest root of the equation x ^ 3-49x = 0

To find the smallest root of the equation x ^ 3 – 49x = 0, solve the given equation.

Factor out the common factor. Common factor x.

x (x ^ 2 – 49) = 0.

Factor the expression in parentheses using the abbreviated multiplication formula for the difference of squares.

x (x – 7) (x + 7) = 0.

To find all the roots of the equation, we turn to solving three linear equations:

1) x = 0.

2) x – 7 = 0;

x = 7;

3) x + 7 = 0;

x = – 7.

Let us choose the smallest of the obtained roots of the equation.

The roots of the equation are x = 0; x = 7 and x = -7.

The smallest is x = – 7.

Answer: x = – 7.