anonymous
  • anonymous
hard Calculus I Question!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Psymon
  • Psymon
Oh snap!
anonymous
  • anonymous
If \[x _{1}, x _{2}\] are the solutions of the equation \[8^{3x ^{2}}=\frac{ 1 }{ 64^{5x+3} }\] Compute the value of \[\left| x _{1}-x _{2} \right|\]
anonymous
  • anonymous
first determine the quadratic which may be some waht 2x^2 =-2*(5x+3)

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More answers

anonymous
  • anonymous
(x1 -x2)^2 =(x1+x2)^2 -4x1.x2
abb0t
  • abb0t
@nincompoop
anonymous
  • anonymous
@matricked the first thing you wrote: 2x^2=-2(5x+3) where did you get that?
anonymous
  • anonymous
I understand the 5x+3, but I don't know where you got 2x^2=-2
anonymous
  • anonymous
see 64^(5x+3)=(8^2)^(5x+3) =8^(2(5x+3)) hence 1/( 8^(2(5x+3) ) = 8^( - 2(5x+3)) hope u get it now
anonymous
  • anonymous
@matricked why did you want to make the exponent negative?
tkhunny
  • tkhunny
It's in the denominator. Did we start with 2x^2 or 3x^2?
anonymous
  • anonymous
@tkhunny as the letters are small it s bit confused whether its 2x^2 or 3x^2
Yttrium
  • Yttrium
Hey, can't we simplify the 8 into 2^3?
anonymous
  • anonymous
@pancakeslover as 1/ (a^n) =a^(-n)
anonymous
  • anonymous
@Yttrium yup we can but it will make us calculate/simplify more
tkhunny
  • tkhunny
Asolutely NO!!!! \(2^{3}\) is NOT a simplification of \(8\). Words mean things. Deliberately making it more complicated cannot be simplified.
anonymous
  • anonymous
\[8^{3x ^{2}}=8^{-10x-6}\] Am I on the right track?
anonymous
  • anonymous
so if they both have the same base, does that mean \[3x ^{2}=-10x-6\]
Yttrium
  • Yttrium
yes you are. :))
anonymous
  • anonymous
great! can you guys tell me what to do next?
Yttrium
  • Yttrium
Solve for x
anonymous
  • anonymous
@Yttrium stick around so I can check with you
anonymous
  • anonymous
@Yttrium so do I use the quadratic formula for this equation? \[3x ^{2}+10x+6\]
Yttrium
  • Yttrium
Yes you can. :)
anonymous
  • anonymous
so now I have \[\frac{ -10\pm \sqrt{28} }{ 6 }\]
anonymous
  • anonymous
@Yttrium I need to compute the value of \[\left| x _{1}-x _{2} \right|\]
Yttrium
  • Yttrium
Yes, you're doing it right. :))
anonymous
  • anonymous
haha thanks. what do I do next?
Yttrium
  • Yttrium
You already have the value of your \[x _{_{1}} and x _{2}\], right? then do the arithmetic. :) You're approaching the final answer.
anonymous
  • anonymous
so once I simplify I get \[\frac{ -5-\sqrt{7} }{ 3 }\] and \[\frac{ -5+\sqrt{7} }{ 3 }\]
anonymous
  • anonymous
@Yttrium I don't know what to do next? how do I know which one is \[x _{1}\]and \[x _{2}\]
Yttrium
  • Yttrium
You can use your any of them since we are dealing with absolute values. Waht ever the x1 and x2, you will arrive at the same answer.
anonymous
  • anonymous
ooh right!! thank you!
anonymous
  • anonymous
@Yttrium is the answer \[\frac{ 10\sqrt{7} }{ 3 }\] ?
anonymous
  • anonymous
@Yttrium wait!
anonymous
  • anonymous
I did that wrong..I added
anonymous
  • anonymous
alright..nevermind I'm still a little confused
Yttrium
  • Yttrium
What's your final answer, then?
anonymous
  • anonymous
@Yttrium \[\left| \frac{ -5+\sqrt{7} }{ 3 }-\frac{ -5-\sqrt{7} }{ 3 } \right|\]
anonymous
  • anonymous
does it all become positive? sorry I have a little trouble with absolute value
Yttrium
  • Yttrium
Yes, because you are dealing a fraction with common denominator. It's like \[\frac{ (-5+\sqrt{7}) }{ 3 } - \frac{ (-5-\sqrt{7}) }{ 3 }\]
anonymous
  • anonymous
@Yttrium thank you for all your help! i got the answer and it's right! you're awesome!
Yttrium
  • Yttrium
No problem. Just post question whenever you get confused again. :))

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