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October 25th, 2014, 07:38 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  range of values.
Find the range of values of x for 3(x^2+5)<7x5. I'm stucked at 3x^27x+20<0 How to continue? 
October 25th, 2014, 09:11 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,884 Thanks: 1503  
October 25th, 2014, 10:50 AM  #3 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  $\displaystyle \color{blue}{3(x^25)<7x5\Longleftrightarrow\ 3x^2157x+5<0\ \Longleftrightarrow\ 3x^27x10<0 \\\;\\ f(x)=3x^27x10,\ \ \ f(x)<0 \ \Longrightarrow\ x\in(x_1,\ x_2), \ with\ \ x_1,\ x_2 \ the \ roots\ of\ the \ equation\ \ f(x)=0 . \\\;\\ \Delta = 49+120=169 \\\;\\ x_{1,\ 2}=\dfrac{b\pm\sqrt{\Delta}}{2a} \\\;\\ x_{1,\ 2}=\dfrac{7\pm\sqrt{169}}{2\cdot3}=\dfrac{7\pm13}{ 6} \\\;\\ x_1 = \dfrac{713}{6}=\dfrac{6}{6}=1 \\\;\\ x_2 = \dfrac{7+13}{6}=\dfrac{20}{6}^{(2}=\dfrac{10}{3} \\\;\\ 3x^27x10<0\ \Longrightarrow\ x\in\left(1,\ \dfrac{10}{3}\right)} $ Last edited by aurel5; October 25th, 2014 at 10:59 AM. 
October 25th, 2014, 10:57 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,884 Thanks: 1503  
October 25th, 2014, 11:10 AM  #5 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  $\displaystyle 3(x^2+5)<7x5\ \Longrightarrow\ x\in\varnothing$ Last edited by aurel5; October 25th, 2014 at 11:14 AM. 
October 25th, 2014, 12:54 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,884 Thanks: 1503  
October 25th, 2014, 11:35 PM  #7 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  
October 26th, 2014, 01:43 AM  #8 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
I don't really understand. So what's the answer?

October 26th, 2014, 01:47 AM  #9 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
$\displaystyle 1<x<\frac{10}{3}$ What are you guys fighting for? Well, at least you give me a good laugh. 
October 26th, 2014, 03:13 AM  #10 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  

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