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October 25th, 2014, 07:38 AM   #1
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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?
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October 25th, 2014, 09:11 AM   #2
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Originally Posted by jiasyuen View Post
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?
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October 25th, 2014, 10:50 AM   #3
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$\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.
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October 25th, 2014, 10:57 AM   #4
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Quote:
Originally Posted by aurel5 View Post
$\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.
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October 25th, 2014, 11:10 AM   #5
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$\displaystyle 3(x^2+5)<7x-5\ \Longrightarrow\ x\in\varnothing$

Last edited by aurel5; October 25th, 2014 at 11:14 AM.
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October 25th, 2014, 12:54 PM   #6
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$\displaystyle 3(x^2+5)<7x-5\ \Longrightarrow\ x\in\varnothing$
thanks for letting the OP figure that out on his own.
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October 25th, 2014, 11:35 PM   #7
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thanks for letting the OP figure that out on his own.
It is convenient to believe that exist a typo,

somewhere out there.
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October 26th, 2014, 01:43 AM   #8
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I don't really understand. So what's the answer?
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October 26th, 2014, 01:47 AM   #9
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$\displaystyle -1<x<\frac{10}{3}$

What are you guys fighting for? Well, at least you give me a good laugh.
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October 26th, 2014, 03:13 AM   #10
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Originally Posted by Monox D. I-Fly View Post
[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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