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Cauchy-schwarz inequality.

Raghav Vaidyanathan you should see this.

Note by Trishit Chandra
1 year, 10 months ago

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I do not think that you can add the inequalities. The thing is that the three inequalities that you have added do not take minimum value for the same x and y. If all the three took minimum value for same x and y, then we could say that LHS is greater than or equal to 17root2. But now we can only say that it is strictly greater than 17root2.

Thank you for taking the time to put this up. Raghav Vaidyanathan · 1 year, 10 months ago

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@Raghav Vaidyanathan Indeed. What he has shown is that \( 17 \sqrt{2} \) is a lower bound. However, he has not shown that this is the maximum possible lower bound, which would then be the minimum of the function.

For example, it is obvious that \( \sqrt{ x^2 + 144 } \geq 0 \) and \( \sqrt{ y^2 + 25 } \geq 0 \), which tells us that \( \sqrt{ x^2 + 144 } + \sqrt{ y^2 + 25 } \geq 0 \). But clearly, 0 is merely a lower bound of the expression, and is not equal to the minimum value of this function. Calvin Lin Staff · 1 year, 10 months ago

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@Raghav Vaidyanathan Ok I've understood this. And trying the problem to solve geometrically. Trishit Chandra · 1 year, 10 months ago

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