Solve the equation (x-7) ^ 4-16 = 0 if the equation has more than one root, then in the answer indicate the sum of all its roots.

Move the number 16 to the right side of the equation (remembering to change the minus to plus):

(x – 7) ^ 4 – 16 = 0.

(x – 7) ^ 4 = 16.

Let’s represent the number 16 as the number 2 to the fourth power:

16 = 24 and 16 = (-2) ^ 4 (since the degree is even).

Two equations are obtained:

1) (x – 7) ^ 4 = 24. The exponents are equal, which means that the bases of the exponent are also equal.

Hence x – 7 = 2;

x = 2 + 7;

x = 9.

2) (x – 7) ^ 4 = (-2) ^ 4.

Hence x – 7 = -2;

x = -2 + 7;

x = 5.

It turned out two roots of the equation: 9 and 5. Their sum is 9 + 5 = 14.

Answer: 14.