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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)<7x-5. I'm stucked at 3x^2-7x+20<0 How to continue?
October 25th, 2014, 09:11 AM   #2
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 Originally Posted by jiasyuen Find the range of values of x for 3(x^2+5)<7x-5. I'm stucked at 3x^2-7x+20<0 How to continue?
check the value of the discriminant, $\displaystyle b^2-4ac$ ... What does that tell you?

 October 25th, 2014, 10:50 AM #3 Senior Member     Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177 $\displaystyle \color{blue}{3(x^2-5)<7x-5\Longleftrightarrow\ 3x^2-15-7x+5<0\ \Longleftrightarrow\ 3x^2-7x-10<0 \\\;\\ f(x)=3x^2-7x-10,\ \ \ f(x)<0 \ \Longrightarrow\ x\in(x_1,\ x_2), \ with\ \ x_1,\ x_2 \ the \ roots\ of\ the \ equation\ \ f(x)=0 . \\\;\\ \Delta = 49+120=169 \\\;\\ x_{1,\ 2}=\dfrac{-b\pm\sqrt{\Delta}}{2a} \\\;\\ x_{1,\ 2}=\dfrac{7\pm\sqrt{169}}{2\cdot3}=\dfrac{7\pm13}{ 6} \\\;\\ x_1 = \dfrac{7-13}{6}=\dfrac{-6}{6}=-1 \\\;\\ x_2 = \dfrac{7+13}{6}=\dfrac{20}{6}^{(2}=\dfrac{10}{3} \\\;\\ 3x^2-7x-10<0\ \Longrightarrow\ x\in\left(-1,\ \dfrac{10}{3}\right)}$ Last edited by aurel5; October 25th, 2014 at 10:59 AM.
October 25th, 2014, 10:57 AM   #4
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 Originally Posted by aurel5 $\displaystyle \color{blue}{3(x^2-5)<7x-5\Longleftrightarrow\ 3x^2-15-7x+5<0\ \Longleftrightarrow\ 3x^2-7x-10<0}$
uhh ...

Quote:
 Find the range of values of x for 3(x^2+5)<7x-5.

 October 25th, 2014, 11:10 AM #5 Senior Member     Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177 $\displaystyle 3(x^2+5)<7x-5\ \Longrightarrow\ x\in\varnothing$ Last edited by aurel5; October 25th, 2014 at 11:14 AM.
October 25th, 2014, 12:54 PM   #6
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 Originally Posted by aurel5 $\displaystyle 3(x^2+5)<7x-5\ \Longrightarrow\ x\in\varnothing$
thanks for letting the OP figure that out on his own.

October 25th, 2014, 11:35 PM   #7
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 Originally Posted by skeeter thanks for letting the OP figure that out on his own.
It is convenient to believe that exist a typo,

somewhere out there.

 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
October 26th, 2014, 03:13 AM   #10
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 Originally Posted by Monox D. I-Fly [MATH] Well, at least you give me a good laugh.
So, be happy!

Look out,

to frame, implicitly,

of so many others

happiness

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