The difference between the solutions to the equation #x^2 = a# is 30. What is #a#?

1 Answer
Sep 21, 2017

#a = pm 225#

Explanation:

We have: #x^(2) = a#

Let's subtract #a# from both sides of the equation:

#Rightarrow x^(2) - a = 0#

Then, using the difference of two squares identity, we can solve for #x#:

#Rightarrow (x - sqrt(a))(x + sqrt(a)) = 0#

#therefore x = pm sqrt(a)#

Now, the difference between these two solutions of #x# is #30#.

Let's use this fact to find the value of #a#:

#Rightarrow sqrt(a) - (- sqrt(a)) = 30 Rightarrow sqrt(a) + sqrt(a) = 30 Rightarrow 2 sqrt(a) = 30 Rightarrow sqrt(a) = 15 therefore a = 225#

#or#

#Rightarrow - sqrt(a) - sqrt(a) = 30 Rightarrow - 2 sqrt(a) = 30 Rightarrow sqrt(a) = - 15 therefore a = - 225#

Therefore, the value of #a# is either #225# or #- 225#.