Mathematics
8 Online
OpenStudy (anonymous):
HELLLP!!!
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OpenStudy (anonymous):
With?
OpenStudy (anonymous):
\[\sqrt[3]{8x^3-1}=2x-1\]
OpenStudy (anonymous):
u want to solve it?
OpenStudy (anonymous):
Yes, solve for x
OpenStudy (anonymous):
well,find \( (3x-1)^3 \)
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Nnesha (nnesha):
i guess there is a typo
isn't that ???
\[(2x-1)^3\]
OpenStudy (anonymous):
@Nnesha , yes ;)
Nnesha (nnesha):
:) cool :)
OpenStudy (anonymous):
u know it does equal to
\[8x^3 - 1 - 12x^2 + 6x\]
OpenStudy (anonymous):
so the equation would be :
\[8x^3 - 1 = 8x^3 - 1 - 12x^2 + 6x\]
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OpenStudy (anonymous):
can u solve it now?
OpenStudy (anonymous):
Wait, is it possible to simplify the cube root?
OpenStudy (anonymous):
Into \[2x-1\]
OpenStudy (anonymous):
u can use \( a^3 - b^3 = (a-b)(a^2 + b^2 - ab) \) but here it wouldn't help.
OpenStudy (jhannybean):
\[\sqrt[3]{8x^3-1}=2x-1\]\[(\sqrt[3]{8x^3-1})^3 = (2x-1)^3\]
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OpenStudy (jhannybean):
\[8x^3-1 = (2x-1)^3\]\[(a-b)^3 = a^3 -b^3 -3ab(a-b)\]
OpenStudy (anonymous):
@Jhannybean , i was writing as you're now writing ;D
OpenStudy (jhannybean):
Oh really? Haha I just saw it @PFEH.1999 :D
OpenStudy (anonymous):
but no prob , u can continue ;)
OpenStudy (jhannybean):
\[(2x-1)^3 \\ = 8x^3 -1-3(2x)(-1)(2x-1) \\ = 8x^3-1+6x(2x-1) \\ = \boxed{8x^3-1+12x^2-6x}\]
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OpenStudy (jhannybean):
Oop. i took \(b\) as \(-1\) instead of \(1\).
OpenStudy (jhannybean):
Correction: \(8x^3 -1-12x^2+6x\)
OpenStudy (jhannybean):
So you would have: \[8x^3-1= 8x^3 -1-12x^2+6x\]Just group all your like terms togethr and simplify.
OpenStudy (anonymous):
okay
OpenStudy (jhannybean):
So let me know what you get, @science00000 :)
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OpenStudy (anonymous):
this is a way to expand \((2x-1)^3=(2x-1) (2x-1)^2\)
OpenStudy (anonymous):
incase ur more comfortable with quadratic