Mathematics
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OpenStudy (anonymous):
If x-(1/x)=1 then (x^4-(1/x^2))/3x^2+5x-3 is
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OpenStudy (anonymous):
3x^2+5x-3 can be written as divided it by x so 3x+5-3/x
3(x-1/x)+5 so it is 8
OpenStudy (anonymous):
then numerator (x^2-1/x)^2
OpenStudy (anonymous):
i feel numerator i am not getting
OpenStudy (anonymous):
(x^2-1/x)(x^2+1/x)so we get x^4-1/x^2
OpenStudy (gorv):
yeah it is
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OpenStudy (anonymous):
how to get numerator to x-1/x format
OpenStudy (gorv):
(x^4-1)/x^2=
OpenStudy (gorv):
u know x^4-1=(x^2-1)*(x^2+1)
OpenStudy (gorv):
and it is divided by x^2 in Q
OpenStudy (anonymous):
(x^2)^2-(1/x)^2 so
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OpenStudy (gorv):
\[\frac{ x^2-1 }{ x }*\frac{ x^2+1}{ x }\]
OpenStudy (gorv):
x^2=x*x take one x below each factor
OpenStudy (anonymous):
latex not working
OpenStudy (gorv):
\[\frac{ x^2-1 }{ x }=\frac{ x^2 }{ x }-\frac{ 1 }{ x }\]
OpenStudy (gorv):
x-1/x
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OpenStudy (anonymous):
1*1
OpenStudy (anonymous):
1/8
OpenStudy (gorv):
other part
\[\frac{ x^2 +1}{ x}=\frac{ x^2 }{ x }+\frac{ 1 }{ x }\]
OpenStudy (gorv):
x+1/x
OpenStudy (anonymous):
yes i was thinking about that only
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OpenStudy (gorv):
numerator
\[(x-\frac{ 1 }{ x})*(x+\frac{ 1 }{ x })\]
OpenStudy (anonymous):
x=1+1/x so x+1/x=x
OpenStudy (gorv):
(x-1/x)^2=1
OpenStudy (anonymous):
so it is 1/8
OpenStudy (gorv):
wait
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OpenStudy (anonymous):
something went wrong over here
OpenStudy (gorv):
x^2+1/x^2-2=1
x^2+1/x^2=1+2=3
OpenStudy (anonymous):
yes
OpenStudy (gorv):
but (x+1/x)^2=x^2+1/x^2+1
OpenStudy (gorv):
but we know x^2+1/x^2 =3 we calculated just above
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OpenStudy (anonymous):
there also 2 insead of 1
OpenStudy (gorv):
(x+1/x)^2=3+2=5
OpenStudy (gorv):
that will be 2 ..typin mistake
OpenStudy (gorv):
x+1/x=sqrt5
OpenStudy (gorv):
1*sqrt5/8 is ans
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OpenStudy (anonymous):
no
OpenStudy (gorv):
what??
OpenStudy (anonymous):
yes see (x^2-1/x)*(x^2+1/x)
OpenStudy (gorv):
that will be x^2 not x
OpenStudy (anonymous):
(x^2)^2-(1/x)^2
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OpenStudy (anonymous):
how
OpenStudy (gorv):
\[\frac{ x^4-1 }{ x^2}=\frac{ x^4}{ x^2 }-\frac{ 1 }{ x^2 }\]
OpenStudy (gorv):
got me ??
OpenStudy (anonymous):
\[\frac{ x^4-1 }{ x^2}=\frac{ x^4}{ x^2 }-\frac{ 1 }{ x^2 }\].i can only see this
OpenStudy (anonymous):
ohh i cant able to see do u calculation without using latex
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OpenStudy (gorv):
\[\frac{ x^4 }{ x^2 }= x^2\]
OpenStudy (gorv):
\[x^2-\frac{ 1 }{ x^2 }=(x-\frac{ 1 }{ x })*(x+\frac{ 1 }{ x })\]
OpenStudy (anonymous):
if we divide it by x^2 then 1/x becomes1/x^3
OpenStudy (anonymous):
x^4-1/x^2 yes
OpenStudy (gorv):
how ????
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OpenStudy (gorv):
(x^4-1)/x^2
OpenStudy (gorv):
here x^2 divide whole term
OpenStudy (anonymous):
see the question above
OpenStudy (gorv):
(x^4-1/X^2)????
OpenStudy (anonymous):
(x^4-(1/x^2))/3x^2+5x-3
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OpenStudy (gorv):
ohhhhhhh
OpenStudy (gorv):
sorryyy i think x^2 DIVID E WHOLE
OpenStudy (anonymous):
ohh very sorry u understood like that ah
OpenStudy (gorv):
thn u did right
OpenStudy (gorv):
above
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OpenStudy (anonymous):
then proceed to get x-1/x
OpenStudy (gorv):
x-1/x=1
1/x=x-1
OpenStudy (gorv):
put this in that equation
OpenStudy (anonymous):
(x^2-(1/x))*(x^2+(1/x)) so
(x^2)^2-(1/x)^2
OpenStudy (gorv):
x-1/x=1
x-1=1/x
put x-1 in place of 1/x
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OpenStudy (gorv):
(x^2-1/x)(x^2+1/x)
OpenStudy (gorv):
(x^2-(x-1))(x^2+x-1)
OpenStudy (anonymous):
then we get x^4-x^2+1
OpenStudy (gorv):
(x^2-x+1)(x^2+x+1)
now
x^2-x+1=x(x-1+1/x)
OpenStudy (anonymous):
ohh yes
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OpenStudy (anonymous):
x^4-x^2+2x-1
divide by x^2
we get x^2-1+2/x-1/x
OpenStudy (anonymous):
sorry x^2-1+2/x-1/x^2
OpenStudy (anonymous):
x-1=x
OpenStudy (anonymous):
wrong now also x-(1/x)
OpenStudy (anonymous):
x-(1/x)=1
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OpenStudy (anonymous):
1/x=x+1 okay
OpenStudy (gorv):
x-1
OpenStudy (anonymous):
(x-1)/x=1
so x-1=x right
OpenStudy (anonymous):
1/x=x+1
OpenStudy (gorv):
x-(1/x)=1
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OpenStudy (anonymous):
can we call ganeshie
OpenStudy (anonymous):
yes
OpenStudy (gorv):
sure u can if u want :)
OpenStudy (anonymous):
x^2-1/x^2-1-2/x
OpenStudy (gorv):
frm where u get this ??
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OpenStudy (anonymous):
x^4-x^2-2x-1
divide by x^2
OpenStudy (anonymous):
(x^2-x-1)(x^2+x+1)
OpenStudy (gorv):
yeah
OpenStudy (gorv):
we didnt get by nowwht we want
OpenStudy (anonymous):
(x^2-x-1)(x^2+x+1)
x^4-x^2-2x-1
divide by x^2
x^2-1/x^2-1-2/x
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OpenStudy (gorv):
x^2-1/x^2=(x-1/x)(x+1/x)
OpenStudy (gorv):
x-1/x=1
OpenStudy (gorv):
x+1/x-1-2/x=x-1-1/x
OpenStudy (gorv):
x-1/x=1
1-1=0
OpenStudy (gorv):
rosy got it ??
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OpenStudy (anonymous):
no we didnt get it i think
OpenStudy (anonymous):
@ganeshie8
ganeshie8 (ganeshie8):
its hard to go through above work as so much was done above, but it seems u had a very good start in killing the denominator