Question

If x be the mean proportional of x-2 and x+6 then find x

Answer 1

x² = (x-2)(x+6)    
 ∴ x² = x² + 6x - 2x - 12
 ∴ x² = x² + 4x - 12
∴ x² - x² = 4x -12
 ∴0 = 4x -12
 ∴4x = -12                                                            
∴ x = -12÷4
∴x = -3

Answer 2

The value of x is 3.

* When a number, x is said to be the mean proportional of two other numbers( a and b), it means that the number, x lies in between a and b.

So, we can write as:

(x-2)/x = x/(x+6)

Or, x² = (x-2)(x+6)

Or, x² = x² + 6x - 2x - 12

Or, x² = x² + 4x - 12

Or, 4x -12 = 0

Or, 4x = 12

Therefore, x = 3

So, we can say that 3 is the mean proportional of two numbers 1 and 9.