Answer:
u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0
Step-by-step explanation:
(x²-1)² - 11(x²-1) + 24 = 0
Evaluate each equation by substituting the value of u to match the equation above.
1) u² - 11u + 24 = 0 where u = (x² - 1)
(x²-1)² - 11(x²-1) + 24 = 0
This equation matches (x²-1)² - 11(x²-1) + 24 = 0
2) (u²)² - 11(u²) + 24 where u = (x² - 1)
[(x²-1)²]² - 11(x²-1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
3) u² + 1 - 11u +24 = 0 where u = (x² - 1)
(x² - 1)² + 1 - 11(x²-1) + 24 = 0
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)
[(x²-1)²-1]² - 11(u² - 1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.
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