The solutions of the equation [tex]4(3x-3)^{\frac{2}{3} } = 36[/tex] are x = 10 and x = - 8.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
[tex]4(3x-3)^{\frac{2}{3} } = 36[/tex]
Now, divide each side of the equation by 4.
[tex]\frac{4(3x-3)^{\frac{2}{3} }}{4}=\frac{36}{4}[/tex]
[tex](3x-3)^{\frac{2}{3} } = 9[/tex]
Cubing the above equation.
[tex]((3x-3)^{\frac{2}{3} })^{3}=(9)^{3}[/tex]
( 3x - 3 )² = 729
3x - 3 = ( √729 )
3x - 3 = ± 27
Now,
3x - 3 = 27
3x = 30
x = 10
and;
3x - 3 = - 27
3x = - 24
x = - 8
Checking for extraneous solutions,
x = 10
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(10)-3)^{\frac{2}{3} }=36\\4(27)^{\frac{2}{3} }=36\\27^{\frac{2}{3} }=9\\(3^{3})^{\frac{2}{3} } = 9\\3^{2}=9\\9=9[/tex]
When x = - 8,
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(-8)-3)^{\frac{2}{3}}=36\\(-27)^{\frac{2}{3}}=9\\(-27)^{2}=(9)^{3}\\729=729[/tex]
The solutions for the equation are x = 10 and x = - 8.
Learn more about equations here:
https://brainly.com/question/2972832
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