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If (a^(2))/(2)=2a, then a equals...

If `(a^(2))/(2)=2a`, then a equals

A

0 or -2

B

0 or 2

C

0 or -4

D

0 or 4

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \(\frac{a^2}{2} = 2a\), we can follow these steps: ### Step 1: Write the equation We start with the given equation: \[ \frac{a^2}{2} = 2a \] ### Step 2: Eliminate the fraction To eliminate the fraction, we can multiply both sides of the equation by 2: \[ 2 \cdot \frac{a^2}{2} = 2 \cdot 2a \] This simplifies to: \[ a^2 = 4a \] ### Step 3: Rearrange the equation Next, we rearrange the equation to bring all terms to one side: \[ a^2 - 4a = 0 \] ### Step 4: Factor the equation Now, we can factor the left-hand side: \[ a(a - 4) = 0 \] ### Step 5: Solve for \(a\) Setting each factor equal to zero gives us the possible solutions: 1. \(a = 0\) 2. \(a - 4 = 0 \Rightarrow a = 4\) ### Conclusion Thus, the values of \(a\) that satisfy the equation are: \[ a = 0 \quad \text{or} \quad a = 4 \]
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