Mean Proportional

The mean proportional between two numbers a and b is a number x such that x/a = b/x. In other words, the mean proportional is the number that satisfies the equation x/a = b/x.

Finding the Mean Proportional

To find the mean proportional between y and 25, we need to solve the equation x/y = 25/x.

Solving the Equation

To solve the equation x/y = 25/x, we can cross-multiply to eliminate fractions:

x^2 = 25y

Now, we can solve for x by taking the square root of both sides of the equation:

x = √(25y)

Substituting the Mean Proportional

Since we are looking for the value of y, we can substitute the mean proportional into the equation:

√(25y)/y = 25/√(25y)

Simplifying the right side of the equation gives us:

√(25y)/y = 5/√y

Now, we can cross-multiply to eliminate fractions and solve for y:

√(25y) * √y = 5y

√(25y^2) = 5y

25y^2 = 25y^2

This equation is always true, which means that y can be any real number.

Conclusion

Since the equation is always true, there is no specific value for y that satisfies the given condition. Therefore, y can be any real number.