Algebra 2 questions

second one is not very difficult..

draw the graph... you have to find the point where x^3-3={x}

so x^3-3 should lie between 0 and 1

so x^3 should lie between 3 and 4

so x should lie betweeen 1 and 2

so {x} = x-1

so the given equation can be rewritten as

x³-3- (x-1) = x³ -x -2 = 0

This will have to be solved by the cos 3 theta trick or the solution to a cubic equation...

The first one seems a geometry problem

Find the real value of the parameter ' t ' for which there is at least one complex number z = x +iy satisfying the condition | z + 3 | = t2 - 2t + 6 and the inequality |z - 3√3 i| < t2

What you can see is find the relation between a and b such that

there is at least one complex number z = x +iy satisfying the condition | z + 3 | = a and the inequality |z - 3√3 i| < b

What will you do??

The distance from the point -3 and 3√3i is 6

so √a+√b should be _____ than 6?

now can you try?