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Standard Deviation about Mean

Bi-conditiona...

Question

Bi-conditional statements are given below. The true statement among them is

5 x - 10 = 0 \Leftrightarrow x = 3

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x^{2} - 16 = 0 \Leftrightarrow (x + 4) (x - 4) = 0

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x^{2} = 1 \Leftrightarrow x = 1

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x^{2} + 9 = 0 \Leftrightarrow x = 3

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Solution

The correct option is B $x^{2} - 16 = 0 \Leftrightarrow (x + 4) (x - 4) = 0$
$x^{2} = 16 - 0 \Rightarrow (x - 4) (x + 4) = 0$
$(x - 4) (x + 4) = 0 \Rightarrow x^{2} - 16 = 0$
$∴ x^{2} - 16 = 0 \Leftrightarrow (x - 4) (x + 4) = 0$
$x = 3$ doesn't mean $5 x - 10 = 0$
$x^{2} - 1$ doesn't mean $x = 1$
$x^{2} + 9 = 0$ doesn't mean $x = 3$

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