# The real numbers #a, b# and #c# satisfy the equation: #3a^2 + 4b^2 + 18c^2 - 4ab - 12ac = 0#. By forming perfect squares, how do you prove that #a=2b=c#?

##### 1 Answer

Dec 5, 2017

#### Explanation:

Notice that the coefficients are all even except for a^2 i.e: 3, rewrite as follow to group for factoring:

We have a perfect square term plus twice perfect square of another term equal to zero, for this to be true each term of the sum must be equal to zero, then:

thus:

Hence proved.