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If a+2b+3c=4, then find the least value ...

If `a+2b+3c=4,` then find the least value of `a^2+b^2+c^2dot`

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To find the least value of \( a^2 + b^2 + c^2 \) given the constraint \( a + 2b + 3c = 4 \), we can use the method of Lagrange multipliers or the Cauchy-Schwarz inequality. Here, we will use the Cauchy-Schwarz inequality for simplicity. ### Step-by-Step Solution: 1. **Set Up the Problem**: We have the equation \( a + 2b + 3c = 4 \) and we want to minimize \( a^2 + b^2 + c^2 \). 2. **Apply the Cauchy-Schwarz Inequality**: According to the Cauchy-Schwarz inequality, we have: \[ ...
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