Mathematics
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OpenStudy (anonymous):
if cos (pie x)=x^2-x-5/4 then the value of x is
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OpenStudy (anonymous):
@ikram002p
OpenStudy (anonymous):
cos pie x=(4x^2-4x-5)/4
OpenStudy (anonymous):
2<=(2x^2-1)<=10
OpenStudy (anonymous):
@waterineyes
OpenStudy (anonymous):
Firstly, I am really \(\color{green}{\textsf{Sorry}}\).. I was busy at some another post.. :(
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OpenStudy (anonymous):
\[\cos (\pi x)=x^2-x-\frac{5}{4}\]
OpenStudy (anonymous):
Is this the question??
OpenStudy (anonymous):
@rosy2 are you there?? Are you alive?? :P
OpenStudy (gorv):
cos will give values between -1 and 1
OpenStudy (gorv):
-1<=(4x^2-4x-5)/4<=1
multiply both side by 4
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OpenStudy (gorv):
-4<(4x^2-4x-5)<4
OpenStudy (gorv):
let forget equal to sign we will add it at the end
OpenStudy (gorv):
now we have 2 equation
-4<4x^2-4x-5
and
4x^2-4x-5<4
OpenStudy (anonymous):
yes @waterineyes ,@gorv i was working on some other problem.
OpenStudy (gorv):
u got upto here??
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OpenStudy (anonymous):
yes
OpenStudy (gorv):
@rosy2
OpenStudy (gorv):
ok can u solve the inequality ??
OpenStudy (gorv):
-4<4x^2-4x-5
add 4 on both side
OpenStudy (gorv):
4x^2-4x-5+4>0
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OpenStudy (gorv):
4x^2-4x-1>0
OpenStudy (gorv):
4x^2-4x-5<4
subtract 4 from both side
OpenStudy (gorv):
4x^2-4x-9>0
OpenStudy (gorv):
we have to solve these 2 equation
OpenStudy (anonymous):
ok i will work and say the solution
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OpenStudy (gorv):
okk..u try n if get a prob we will help u thn
OpenStudy (anonymous):
1/2,(1+or-16sqrt(2))/2
OpenStudy (gorv):
we have to find where they are greater than zero or less than zero
OpenStudy (gorv):
i dont have calc with me right now
OpenStudy (anonymous):
is it correct?
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OpenStudy (gorv):
can i tell u the ans in the eve ??
OpenStudy (anonymous):
okay
OpenStudy (gorv):
4x^2-4x-1>0
\[\frac{ 4\pm \sqrt{(-4)^2-4*4*(-1)} }{ 2*4 }\]
OpenStudy (gorv):
\[\frac{ 4 \pm \sqrt{16+16}}{ 8}\]
OpenStudy (gorv):
\[\frac{ 4 \pm \sqrt{16*2}}{ 8 }=\frac{ 4\pm4\sqrt{2} }{ 8 }\]
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OpenStudy (gorv):
\[\frac{ 1 \pm \sqrt{2}}{ 2}\]
OpenStudy (anonymous):
yes
OpenStudy (anonymous):
\[(4\pm \sqrt{160})/8\]
OpenStudy (anonymous):
\[(1\pm4\sqrt{10})/2\]
OpenStudy (gorv):
very veryy good rosy
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OpenStudy (anonymous):
\[(1\pm4\sqrt{10})/2\]
OpenStudy (gorv):
u did a little mistake
OpenStudy (gorv):
4 will not come before sqrt
OpenStudy (gorv):
\[\frac{ 4 }{ 8} \pm \frac{ 4\sqrt{10} }{ 8 }=\frac{ 1 \pm \sqrt{10}}{ 2 }\]
OpenStudy (gorv):
got me??
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OpenStudy (anonymous):
-9*16=144 add it to 16 we get160 right?