We are given two equations:
1.
2.
Step 1: Solve the first equation The first equation is: Let .
The equation becomes: Factoring the quadratic equation: Thus, or .
Since , we discard and keep .
Therefore: This gives two solutions: or So, the roots of the first equation are and .
Step 2: Solve the second equation The second equation is: Let .
The equation becomes: Substitute into the equation: Now, solve this equation for roots by considering the two cases of the absolute value: Case 1: Multiply both sides by 2: Rearrange: So, . Case 2: Multiply both sides by 2: Rearrange: Use the quadratic formula: Thus, the roots of the second equation are , , and .
Step 3: Calculate the sum of squares of roots The roots of the first equation are and .
Their squares are: The roots of the second equation are , , and .
Their squares are: Thus, the sum of squares of all roots is: