Rewrite the equation in terms of u.
(u
2
+3)u−2=0
u
2
u−2=0
(u
2
+9)u−2=0
u
2
u+1=0
The Correct Answer and Explanation is :
It seems there’s a bit of confusion in the way the equations are written here. Let’s clarify and rewrite each one correctly before finding a solution.
Starting with the possible intended equation formats, let’s consider four equations separately:
- ((u^2 + 3)u – 2 = 0)
- (u^2 \cdot u – 2 = 0)
- ((u^2 + 9)u – 2 = 0)
- (u^2 \cdot u + 1 = 0)
We’ll go through each equation individually to determine which one could be rewritten and solved.
Equation Analysis:
- ((u^2 + 3)u – 2 = 0)
Expanding this:
[
u^3 + 3u – 2 = 0
]
This is a cubic equation in ( u ), and it could potentially have real or complex roots, though solving this would involve either factoring or using numerical methods. - (u^2 \cdot u – 2 = 0)
Simplifying this, we get:
[
u^3 – 2 = 0
]
Solving for ( u ), we find:
[
u^3 = 2 \implies u = \sqrt[3]{2}
]
This is a simple solution with a real value. - ((u^2 + 9)u – 2 = 0)
Expanding this:
[
u^3 + 9u – 2 = 0
]
This is another cubic equation, and like the first, it would likely require numerical methods for exact solutions. - (u^2 \cdot u + 1 = 0)
Simplifying this:
[
u^3 + 1 = 0
]
Solving for ( u ), we get:
[
u^3 = -1 \implies u = -1
]
since (-1) is the cube root of (-1).
Conclusion
From these, Equation 2: (u^2 \cdot u – 2 = 0) provides a straightforward answer, with ( u = \sqrt[3]{2} ) as the real root. This solution doesn’t require complex factors or additional terms, making it the simplest answer among the options.