SOLUTION: Hi, I tried to solve the following problem and this is what I got can someone tell me if its right? 1. 3^1/2(y)^2-4y-(3)^1/2=0 Which is our graphical form 3^1/2y^2-4y-(7(

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi, I tried to solve the following problem and this is what I got can someone tell me if its right? 1. 3^1/2(y)^2-4y-(3)^1/2=0 Which is our graphical form 3^1/2y^2-4y-(7(      Log On


   

Question 154374: Hi,
I tried to solve the following problem and this is what I got can someone tell me if its right?
1. 3^1/2(y)^2-4y-(3)^1/2=0
Which is our graphical form 3^1/2y^2-4y-(7(3)^1/2=0


simplifies to 3/2y^2-4*y-21/2=0
Explanation:
Look at 3^1/2y^2-4y-(7(3)^1/2=0

Replace constants in factor: 3 ,1 with 3
It becomes 3/ 2*y^2 -4y 7*3^1/2=0

Look at 3/ 2*y^2 -4y 7*3^1/2=0.
Replace constants in factor: {3},1 with 3
It becomes: 3/2*y^2 -4y -7*3/2 =0
Look at: 3 /2*y^2 -4y -7*3/2 =0
Multiplied numerator integers 7*3 to get 21
It becomes 3 /2*y^2 -4y -21/2 =0
Result: 3 / 2*y^2 -4y -21/2=0
Again, I sorry for the trouble I am causing thank you so much for your help.
Jimmy

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know what to make of your work, but here's the way that I would do it:


3%5E%281%2F2%29y%5E2-4y-%283%29%5E%281%2F2%29=0+ Start with the given equation.


sqrt%283%29y%5E2-4y-sqrt%283%29=0+ Rewrite 3%5E%281%2F2%29 as sqrt%283%29



Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=sqrt%283%29, b=-4, and c=-sqrt%283%29



Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


Plug in a=sqrt%283%29, b=-4, and c=-sqrt%283%29


Negate -4 to get 4


y+=+%284+%2B-+sqrt%28+16-4%28sqrt%283%29%29%28-sqrt%283%29%29+%29%29%2F%282%2Asqrt%283%29%29 Square 4 to get 16


y+=+%284+%2B-+sqrt%28+16-4%28-3%29+%29%29%2F%282%2Asqrt%283%29%29 Multiply sqrt%283%29 and -sqrt%283%29 to get -sqrt%283%29sqrt%283%29=-sqrt%283%2A3%29=-sqrt%283%5E2%29=-3



y+=+%284+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2Asqrt%283%29%29 Multiply -4 and -3 to get 12


y+=+%284+%2B-+sqrt%28+28+%29%29%2F%282%2Asqrt%283%29%29 Add


y+=+%284+%2B-+2%2Asqrt%28+7+%29%29%2F%282%2Asqrt%283%29%29 Simplify the square root


y+=+%284+%2B+2%2Asqrt%28+7+%29%29%2F%282%2Asqrt%283%29%29 or y+=+%28-4+-+2%2Asqrt%28+7+%29%29%2F%282%2Asqrt%283%29%29 Break up the "plus/minus"



or y+=+%28%284+-+2%2Asqrt%28+7+%29%29%2F%282%2Asqrt%283%29%29%29%28sqrt%283%29%2Fsqrt%283%29%29 Multiply both numerator and denominator by sqrt%283%29 to rationalize the denominator


y+=+%28%28sqrt%283%29%29%284+%2B+2%2Asqrt%28+7+%29%29%29%2F%282%2Asqrt%283%29sqrt%283%29%29 or y+=+%28%28sqrt%283%29%29%284+-+2%2Asqrt%28+7+%29%29%29%2F%282%2Asqrt%283%29sqrt%283%29%29 Combine the fractions


y+=+%28%28sqrt%283%29%29%284+%2B+2%2Asqrt%28+7+%29%29%29%2F%282%2A%283%29%29 or y+=+%28%28sqrt%283%29%29%284+-+2%2Asqrt%28+7+%29%29%29%2F%282%2A%283%29%29 Multiply


y+=+%28%28sqrt%283%29%29%284+%2B+2%2Asqrt%28+7+%29%29%29%2F%286%29 or y+=+%28%28sqrt%283%29%29%284+-+2%2Asqrt%28+7+%29%29%29%2F%286%29 Multiply again


y+=+%284%2Asqrt%283%29+%2B+2%2Asqrt%283%29sqrt%28+7+%29%29%2F%286%29 or y+=+%284%2Asqrt%283%29+-+2%2Asqrt%283%29sqrt%28+7+%29%29%2F%286%29 Distribute



y+=+%284%2Asqrt%283%29+%2B+2%2Asqrt%28+21+%29%29%2F%286%29 or y+=+%284%2Asqrt%283%29+-+2%2Asqrt%28+21+%29%29%2F%286%29 Multiply


y+=+%282%2Asqrt%283%29+%2B+sqrt%28+21+%29%29%2F%283%29 or y+=+%282%2Asqrt%283%29+-+sqrt%28+21+%29%29%2F%283%29 Reduce



================================================================

Answer:


So the solutions are y+=+%282%2Asqrt%283%29+%2B+sqrt%28+21+%29%29%2F%283%29 or y+=+%282%2Asqrt%283%29+-+sqrt%28+21+%29%29%2F%283%29


which approximate to y=2.68223 or y=-0.37282