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1/x^2 + 1/x =6 solve for x
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petewe
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make the left side into 1 equation.
asnaseer
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multiply both sides by\(x^2\) and solve the resulting quadratic equation.
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\[x^2/ x^2 + x^2/x^2 = 6x^2\]
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2x^2 = 6x^2
asnaseer
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the denominator of your second term above is wrong
asnaseer
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you should get:\[x^2/ x^2 + x^2/x = 6x^2\]
asnaseer
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next - simplify each term
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but dont they need to have the same denominator to add
asnaseer
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what does \(x^2/x^2\) equal?
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1
asnaseer
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correct - now simplify the next term
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1
1+ x= 6x^2
asnaseer
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thats right - now re-arrange this into a standard form, i.e into the form \(ax^2+bx+c=0\) and then solve
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1
so I did quadratic equation and go -1 plus or minus radical 25 all over -12
asnaseer
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doesn't look right - can you please show your steps so that I can help spot where you may have made a mistake?
P->Q
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k, u said put it into the standard form so I started from
1 + x = 6x^2
-6x^2 + x+1 = 0
a= -6, b= 1, c= 1
\[-1\pm \sqrt{1^{2}-4(-6)(1) \over 2(-6)}\]
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then got -1 plus or minus radical 25 all over -12
asnaseer
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oh - sorry - I misread
asnaseer
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you are right - and you know what \(\sqrt{25}\) equals?
asnaseer
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the formula you used doesn't look quite right, it should be:\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
asnaseer
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the WHOLE thing should be divided by 2a
asnaseer
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so you should have got:\[\frac{-1\pm \sqrt{1^{2}-4(-6)(1)}}{2(-6)}\]
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o ok so um x = 1/-3 and x = 1/2
asnaseer
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perfect!
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ya I ment to put all over 2a but I was trying to make it come out nice and pretty in the equation thing but it took lng
asnaseer
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although you should write it as:
x=-1/3 or 1/2
asnaseer
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you don't usually put the minus sign in the denominator
P->Q
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wow these are so frustrating I was literally about to give up and go home, im in a library trying to study and there are all these other students basically hanging out and talking and there are no available tutors
asnaseer
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also note that you should use the word "or" rather than "and" here.
i.e. x = -1/3 or 1/2
instead of x = -1/3 and 1/2
because x canot equal both values at the same time
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ok ill do that
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thanks a lot you gave me a little hope to keep pushing a little more
asnaseer
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great - and keep persevering - you'll get the hang of these very soon I'm sure :)
asnaseer
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yw :)