Mathematics, 20.07.2019 17:00 tayjohn9774

What is the solution to the equation ^3sqrt m-4- ^3sqrt 2m+8=0 a. m= -24 b. m= -12 c. m= -6 d. m= -4

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The correct answer is: [B]: " m = -12 " .
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Explanation:
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Given the equation:

→   " ³√(m − 4) − ³√(2m + 8) = 0 " ; Solve for "m" ;

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We start by rewriting the terms in the equation:
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Note the following property of exponents:
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→ "  a ⁽ ˣ / ʸ⁾ = ʸ√(aˣ) ; { y $\neq$ 0 } " ;
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So, rewrite: "   ³√(m − 4) " ; as: " (m − 4) ⁽ ¹/³⁾ " ;

and rewrite: "    ³√(2m + 8) " ; as: " (2m + 8) ⁽ ¹/³⁾ " ;
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And rewrite the question as:
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→ " (m − 4) ⁽ ¹/³⁾   − (2m + 8) ⁽ ¹/³⁾ = 0 " ; Solve for "m" ;
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Add " (2m + 8) ¹/³ " to EACH SIDE of the equation; as follows:
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→ (m − 4) ¹/³⁾  −  (2m + 8)¹/³  +  (2m + 8) ¹/³ = 0 + (2m + 8) ¹/³ ;

to get:
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→ " (m − 4) ¹/³ = (2m + 8) ¹/³ " ;
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→ { Note: If " x ⁿ =   y ⁿ ; then " x = y " .} .
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→   "  m − 4 = 2m + 8 " ; Solve for "m" ;
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Subtract "2m" from each side of the equation; & add "4" to each side of the equation; as follows:
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        m − 4 − 2m + 4 = 2m + 8 − 2m + 4 ;

to get:
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→ -1m = 12 ;

Now, divide each side of the equation by "-1 " ;
to isolation "m" on one side of the equation; & to solve for "m" ;

  → -1m / -1 = 12 / -1 ;
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to get:
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" m = -12 " ;

→ which is: Answer choice: [B]: " m = -12 " .
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Hope this helps!
Best wishes.
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Answer from: Quest

picture below

Answer from: Quest

Uh idk bossman just do it lol

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What is the solution to the equation ^3sqrt m-4- ^3sqrt 2m+8=0 a. m= -24 b. m= -12 c. m= -6 d. m= -...