Set up an equation and solve each of the following problems. The cube of a number equals nine times the same number. Find the number.

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Maciej Morrow · Accepted Answer

Step 1  An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.  Step 2  Given cube of a number equal to nine times of the same number. Let us assume the number as variable x. Then cube of the number is x3 and nine times of the same number will be 9x. Equate both the terms to solve for the number x as follows;  x3=9x  x3−9x=9x−9x .................. Subtract 9x from both sides.  x(x2−9)=0 .................... Take the common term out,  x(x2−33)=0  x(x−3)(x+3)=0 .................... Use (a2−b2)=(a2−b2)=(a−b)(a+b).  x=0 or (x−3)=0 or (x+3)=0 ....................... Seperate the factors.  x=0 or x=3 or x=−3  Hence, the numbers satisfying the given condition are 0 or ±3.

Set up an equation and solve each of the following problems. The cube of a numbe

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