Solve the following equation using an appropriate substituti

Solve the following equation using an appropriate substitution. Check your answers

(x^2-4)^2-(x^2-4)-12=0

Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)

Solution :

Here;

(x^2-4)^2-(x^2-4)-12=0

Let x^2-4 = t

=> t² -t-12 = 0

=> (t-4)(t+3) = 0

=> t = 4 and -3

=> x²-4 = 4 and x²-4 = -3

=> x² = 8 and x² = 1

=> x = -22 , +22 , -1 , +1

or x = {-2.828 , +2.828 , -1 , +1}