SOLUTION: Quadratic Formula: Solve 3 = 5/x + 4/x^2 they say the answer is 5 + or - sqrt of 73 / 6, I get -5 + or - sqrt of 73 over 8. Please walk me thru each step. Thanks

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Quadratic Formula: Solve 3 = 5/x + 4/x^2 they say the answer is 5 + or - sqrt of 73 / 6, I get -5 + or - sqrt of 73 over 8. Please walk me thru each step. Thanks      Log On


   

Question 402303: Quadratic Formula: Solve
3 = 5/x + 4/x^2
they say the answer is 5 + or - sqrt of 73 / 6, I get -5 + or - sqrt of 73 over 8. Please walk me thru each step. Thanks
Found 4 solutions by Earlsdon, sofiyac, Edwin McCravy, Mr.Math:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
3+=+%285%2Fx%29%2B%284%2Fx%5E2%29 Multiply through by x%5E2
3x%5E2+=+5x%2B4 Rewrite as:
3x%5E2-5x-4+=+0 Solve with the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a and here, a = 3, b = -5, and c = -4.
x+=+%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%283%29%28-4%29%29%29%2F2%283%29 Do the math.
x+=+%285%2B-sqrt%2825%2B48%29%29%2F6
x+=+%285%2B-sqrt%2873%29%29%2F6

Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
ok so this one is tricky, first thing i would do is multiply everything by x%5E2
so you get
3x%5E2=5x%2B4 now move everything to left side
3x%5E2-5x-4=0 now plug in the values
a=3, b=-5, c=-4
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29+
x+=+%285+%2B-+sqrt%28+25%2B48+%29%29%2F%286%29+
x+=+%285+%2B-+sqrt%28+73+%29%29%2F%286%29+
YAY!

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
3%22%22=%22%225%2Fx%22%22%2B%22%224%2Fx%5E2


Multiply through by LCD = x² to clear of fractions


red%28x%5E2%29%2A3%22%22=%22%22red%28x%5E2%29%2Aexpr%285%2Fx%29%22%22%2B%22%22red%28x%5E2%29%2Aexpr%284%2Fx%5E2%29

3x%5E2%22%22=%22%22red%28x%5Ecross%282%29%29%2Aexpr%285%2Fcross%28x%29%29%22%22%2B%22%22red%28cross%28x%5E2%29%29%2Aexpr%284%2Fcross%28x%5E2%29%29

3x%5E2%22%22=%22%225x%22%22%2B%22%224

Get 0 on the right and the left in descending order:

3x%5E2%22%22-%22%225x%22%22-%22%224%22%22=%22%220

Compare that to:

ax%5E2%22%22%2B%22%22bx%22%22%2B%22%22c%22%22=%22%220

and we see that

a=3, b=-5, c=-4

So we substitute in:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2-4%2A%283%29%2A%28-4%29+%29%29%2F%282%2A%283%29%29+

x+=+%285+%2B-+sqrt%2825%2B48%29%29%2F6+
 
x+=+%285+%2B-+sqrt%2873%29%29%2F6+

Edwin

Answer by Mr.Math(29) About Me  (Show Source):
You can put this solution on YOUR website!
x <> 0, so multiply equation on x^2 :
3x%5E2+=+5x+%2B+4
3x%5E2+-+5x+-+4+=+0
D+=+25+-+4%2A3%2A%28-4%29+=+25+%2B+48+=+73
x+=+%285+%2B-+sqrt+%2873%29%29+%2F+6