Question

If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.
What number must be added to each of the numbers 16, 26 and 40 so that the resulting
numbers may be in continued proportion?
Find two numbers such that the mean proportional between them is 28 and the third​

Answer 1

Answer:

1. x+2 : x+5 :: x+5 : x+9

=> (x+5)² = (x+2)(x+5)

=> x²+25+10x = x²+2x+5x+10

=> x²-x²+25-10+10x-2x-5x= 0

=> 15+3x = 0

=> 3x = -15

=> x = -3

2.