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How do you solve #2(x-2)^(2/3) = 50#?

Answer 1

Avery Alexander

If #2(x-2)^(2/3) = 50# then #(x-2)^(2/3) = 25#

If we cube both sides we get #(x-2)^2 = 25^3 = 25^2*5^2#

or #(x-2)^2 - 125^2 = 0#

remember that anything of the form #(a^2-b^2)# can be factored as #(a-b)(a+b)#

we have #((x-2)-125)((x-2)+125) = 0# or #(x-127)(x+123)=0#

so #x=127# or #x=-123#

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Answer 2

Eva Abramson

To solve the equation 2(x-2)^(2/3) = 50, you can follow these steps:

Divide both sides of the equation by 2: (x-2)^(2/3) = 25.
Cube both sides of the equation to eliminate the fractional exponent: [(x-2)^(2/3)]^3 = 25^3.
Simplify the left side of the equation: (x-2)^2 = 25^3.
Take the square root of both sides to remove the exponent: √[(x-2)^2] = √(25^3).
Simplify the equation: x-2 = 25√25.
Evaluate the square root of 25: x-2 = 25 * 5.
Simplify the equation: x-2 = 125.
Add 2 to both sides of the equation: x = 125 + 2.
Solve the equation: x = 127.

Therefore, the solution to the equation 2(x-2)^(2/3) = 50 is x = 127.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.