Final answer:
To find the value of m⁴ + 1/m⁴, square the given equation m - 1/m = 3. Then square the resulting equation again. Simplify the equation to find the value of m⁴ + 1/m⁴, which is 167.
Step-by-step explanation:
To find the value of m⁴ + 1/m⁴, we need to substitute the value of m - 1/m into the expression. We are given that m - 1/m = 3.
Let's square the equation m - 1/m = 3: (m - 1/m)² = 3². Expanding and simplifying, we get m² + 1/m² - 2 = 9.
Now let's square this equation one more time: (m² + 1/m² - 2)² = 9². Expanding and simplifying, we get m⁴ + 1/m⁴ + 4 - 4(m² + 1/m²) = 81. Since m² + 1/m² is equal to 9 + 2 (from the earlier equation), 4(m² + 1/m²) is 4*(9 + 2). Therefore, the equation becomes m⁴ + 1/m⁴ - 4*(11) + 4 = 81. Simplifying further, we have m⁴ + 1/m⁴ = 81 - 4 + 4*(11), which equals 167.