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

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Answer 1 · 2017-09-21T17:01:02

$a = \pm 225$ $a = pm 225$

We have: $x^{2} = a$ $x^(2) = a$

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

$\Rightarrow x^{2} - a = 0$ $Rightarrow x^(2) - a = 0$

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

$\Rightarrow (x - \sqrt{a}) (x + \sqrt{a}) = 0$ $Rightarrow (x - sqrt(a))(x + sqrt(a)) = 0$

$therefore x = pm sqrt(a)$

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 $- 225$ .

The difference between the solutions to the equation x^2 = ax2=ax^2 = a is 30. What is aaa?