msdjaw wrote:
If \(a - b = 16\) and \(\sqrt{a} + \sqrt{b} = 8\), what is the value of \(\sqrt{ab}\) ?
A. 2
B. 4
C. 8
D. 12
E. 15
Hello!
I have the answer to this question in my book using other methods. However, whenever I try to solve this question using the substitution method, my solution is not the same as what my book says. Would you please be kind enough to solve this question for me using the SUBSTITUTION method?
I know there are easier methods as well but I need to know what mistake I am making by using the substitution method.
Here is an algebraic solution to the problem.
First of all, we need to simplify the question.
Let's say: The sum of two numbers/integers is equal to 8 and the difference between the square of the two numbers/integers is equal to 16. Find the two numbers/integers and calculate the value of the square root of the product of the two numbers/integers.
Let's \(\sqrt{a}\) be the first number/integer and \(\sqrt{b}\) the second number/integer
\(\sqrt{a}+\sqrt{b}=8\)
\(\sqrt{a}^2-\sqrt{b}^2=16\)
\((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) =16\)
\(8(\sqrt{a}-\sqrt{b})=16\)
\(\sqrt{a}-\sqrt{b}=2\)
Then solve the two equations
\(\sqrt{a}+\sqrt{b}=8\)
\(\sqrt{a}-\sqrt{b}=2\)
\(2\sqrt{a}=10\)
\(\sqrt{a}=5\)
\(\sqrt{b}=3\)
Thus, \(a=25\)
and \(b=9\)
\(\sqrt{ab}=\sqrt{25*9}\)
The answer is 15.
I hope that the formula will work