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Different Types of Intervals in Inequality

If x,y∈ Rsa...

Question

If $x, y \in R$ satisfies $(x + 5)^{2} + (y - 12)^{2} - (14)^{2},$ then the minimum value of expression is $- p$ Find p

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Solution

Let $z = (x + 5)^{2} + (y - 12)^{2} - (14)^{2}$
Clearly minimum value of $z$ will occur when first and second term will be zero,
$\Rightarrow x = - 5, y = 12$ , Since square of a real number can be negative.
Hence minimum value of $z$ will be $- (14)^{2} = - 196$

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Different Types of Intervals in Inequality

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