For the second one, take an alternative definition of absolute value,
|x|= then the equation is easily solved as long as you remember to take both positive and negative square root when the time comes
1.Suppose x and y are real numbers. Prove or give a counterexample.
if x + y is irrational, the x is irrational or y is irrational.
I found a counterexample already in a earlier question that asked if x is irrational and y is irrational, then x + y is irrational, but im not sure how to approach this question.
2.If x is a real number, then implies that
for this one, im not sure how to deal with the absolute value.