Maths-

General

Easy

Question

# If A and G are A.M and G.M between two positive numbers a and b are connected by the relation A+G=a-b then the numbers are in the ratio

- 1:3
- 1:6
- 1:9
- 1:12

Hint:

### We know that A.M is Arithmetic Mean and G.M is Geometric Mean and the A.M and G.M for two positive numbers, say a and b will be and √ respectively. We will make a quadratic equation using it and the roots of the equation gives the value of the numbers which we have to prove.

## The correct answer is: 1:9

### Detailed Solution

AM between two positive numbers is given by

GM between two positive numbers a and b is given by

We have been given that :

We have to be careful while solving quadratic equation questions as there are chances of mistakes with the signs while finding the roots. Sometimes the students try to use factorisation methods to solve the quadratic equation, but in this type of questions, it is not recommended at all. Always try to use the quadratic formula for solving. You can also remember the statement to be proved, given in the question as a property for two positive numbers.

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