SOLUTION: ) List the members of each of the sets below: (i) { x:x is a square of an integer and 100<x<300} (ii) {x:x is a solution of the equation x^2 - 6x +4 = 0}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: ) List the members of each of the sets below: (i) { x:x is a square of an integer and 100<x<300} (ii) {x:x is a solution of the equation x^2 - 6x +4 = 0}       Log On


   

Question 609449: ) List the members of each of the sets below:
(i) { x:x is a square of an integer and 100 (ii) {x:x is a solution of the equation x^2 - 6x +4 = 0}
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
i) Since
11%5E2+=+121
12%5E2+=+144
13%5E2+=+169
14%5E2+=+196
15%5E2+=+225
16%5E2+=+256
17%5E2+=+289
The set would be {11, 12, 13, 14, 15, 16, 17}}}

ii) x%5E2-6x%2B4+=+0
Using the Quadratic Formula we get:
x+=+%28-%28-6%29+%2B-+sqrt%28%28-6%29%5E2+-+4%281%29%284%29%29%29%2F2%281%29
which simplifies as follows:
x+=+%28-%28-6%29+%2B-+sqrt%2836+-+4%281%29%284%29%29%29%2F2%281%29
x+=+%28-%28-6%29+%2B-+sqrt%2836+-+16%29%29%2F2%281%29
x+=+%28-%28-6%29+%2B-+sqrt%2820%29%29%2F2%281%29
x+=+%286+%2B-+sqrt%2820%29%29%2F2
x+=+%286+%2B-+sqrt%284%2A5%29%29%2F2
x+=+%286+%2B-+sqrt%284%29%2Asqrt%285%29%29%2F2
x+=+%286+%2B-+2%2Asqrt%285%29%29%2F2
x+=+%282%283+%2B-+sqrt%285%29%29%29%2F2
x+=+%28cross%282%29%283+%2B-+sqrt%285%29%29%29%2Fcross%282%29
x+=+3+%2B-+sqrt%285%29
So the solution set is { 3+%2B+sqrt%285%29  ,  3+-+sqrt%285%29 }