SOLUTION: Algebraically determine the exact roots of each equation. a) sqrt7x-2/sqrt2x = sqrt2x/sqrt7x+2 I got 7x^2-4=2x 7x^2-4-2x^2=0 5x^2-4=0 x=sqrt4/5 My teacher

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Question 118442: Algebraically determine the exact roots of each equation.
a) sqrt7x-2/sqrt2x = sqrt2x/sqrt7x+2
I got 7x^2-4=2x
7x^2-4-2x^2=0
5x^2-4=0
x=sqrt4/5 My teacher marked it wrong .
b)4/x+1 - x+3/x-2 = -5
I got x= -5+or- 311i/8 Also marked wrong.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Algebraically determine the exact roots of each equation.
a) sqrt7x-2/sqrt2x = sqrt2x/sqrt7x+2
I got 7x^2-4=2x
7x^2-4-2x^2=0
5x^2-4=0
x=sqrt4/5 My teacher marked it wrong .
b)4/x+1 - x+3/x-2 = -5
I got x= -5+or- 311i/8
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a) sqrt(7x-2)/sqrt2x = sqrt2x/sqrt(7x+2)
Cross-multiply to get:
sqrt(49x^2-4) = sqrt(4x^2)
49x^2-4 = 4x^2
45x^2 = 4
x^2 = 4/45
x = 2/3sqrt(5)
x = 2sqrt(5)/15
x = (2/15)sqrt(5)
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b)4/(x+1) - (x+3)/(x-2) = -5
Multiply thru by (x+1)(x-2) to get:
4(x-2) - (x+3)(x+1) = -5(x-2)(x+1)
4x-8 -[x^2+4x+3] = -5[x^2-x-2]
4x-8-x^2-4x-3 = -5x^2+5x+10
4x^2-5x-21=0
x = [5 +- sqrt(25-4*4*-21)]/8
x = [5 +- sqrt(361)]/8
x = [5 +- 19]/8
x = 3 or x = -7/4
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Cheers,
stan H.