Pregunta
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\( m = \sqrt[4]{34} \) or \( m = -\sqrt[4]{34} \)
Solución
To find the value of \( m \) in the equation \( m \times m \times m^{2}=34 \), we can simplify the equation first and then solve for \( m \).
Given equation: \( m \times m \times m^{2}=34 \)
Simplifying the equation:
\( m^{3} \times m = 34 \)
\( m^{4} = 34 \)
Now, we need to find the value of \( m \) that satisfies the equation \( m^{4} = 34 \).
Let's solve for \( m \).
Solve the equation by following steps:
- step0: Solve for \(m\):
\(m^{4}=34\)
- step1: Simplify the expression:
\(m=\pm \sqrt[4]{34}\)
- step2: Separate into possible cases:
\(\begin{align}&m=\sqrt[4]{34}\\&m=-\sqrt[4]{34}\end{align}\)
- step3: Rewrite:
\(m_{1}=-\sqrt[4]{34},m_{2}=\sqrt[4]{34}\)
The solutions for \( m \) are \( m = -\sqrt[4]{34} \) and \( m = \sqrt[4]{34} \).
Therefore, the values of \( m \) that satisfy the equation \( m \times m \times m^{2}=34 \) are \( m = -\sqrt[4]{34} \) and \( m = \sqrt[4]{34} \).
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Simplifique esta solución Mind Expander
To solve the equation \( m \times m \times m^{2} = 34 \), we first simplify the left side. We can combine the terms: \[ m \times m \times m^{2} = m^{1} \times m^{1} \times m^{2} = m^{1+1+2} = m^{4} \] So we have: \[ m^{4} = 34 \] To find \( m \), we take the fourth root of both sides: \[ m = \sqrt[4]{34} \] This can be approximated numerically. Since \( 2^4 = 16 \) and \( 3^4 = 81 \), we know \( m \) is between 2 and 3. Calculating further, we find: \[ m \approx 2.34 \] Thus, the approximate value of \( m \) is \( \sqrt[4]{34} \approx 2.34 \).
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