Question

Two numbers and their geometric mean are given. Find the value of \(a\). 4 and \(a ; 14\)

Short answer

The value of \(a\) is 49.

Step-by-step solution

Understand the problem

We need to use the concept of geometric mean. The geometric mean of two positive numbers \(x\) and \(y\) is \(g = \sqrt{xy}\), where \(g\) represents the geometric mean of these two numbers.

Create equation using given values

It is given that the geometric mean of 4 and \(a\) is 14. We set this up as an equation: 14 = \(\sqrt{4*a}\).

Solve the equation to find value of a

Squaring both sides of the equation, we get: 196 = 4*a. Dividing both sides by 4, we get: a = 196 / 4 = 49.