X2 -2(5 m)x 3(7 m)=0 is reciprocal of the other.Find the value of M?

Question

Answer

Solution:

Given equation: x^2 - 2(5m)x + 3(7m) = 0

Let's find the reciprocal of the given equation:

x^2 - 2(5m)x + 3(7m) = 0

Dividing both sides by x^2:

1 - 2(5m)/x + 3(7m)/x^2 = 0

Now, let's find the reciprocal of the above equation:

x^2/3(7m) - x/2(5m) + 1 = 0

This is the reciprocal of the given equation.

Condition for Reciprocal Equations:

The condition for two equations to be reciprocal is that the coefficients of the two equations must be in the same ratio.

Let's apply this condition to the given equation and its reciprocal:

Original equation: x^2 - 2(5m)x + 3(7m) = 0

Reciprocal equation: x^2/3(7m) - x/2(5m) + 1 = 0

Comparing the coefficients of x^2 in both equations:

1 = 1/3(7m)

7m = 3

m = 3/7

Conclusion:

The value of m is 3/7.

Thus, the given equation x^2 - 2(5m)x + 3(7m) = 0 and its reciprocal x^2/3(7m) - x/2(5m) + 1 = 0 are reciprocal of each other when m = 3/7.