If (4a + 7b) (4c – 7d) = (4a – 7b) (4c + 7d), then which one of the following is correct?Options𝒂/𝒃=𝒄/𝒅𝒂/𝒃=𝒅/𝒄𝟒𝒂/𝟕𝒃=𝒄/𝒅𝒂/𝒅=𝒄/𝒃

Question

Options
$\frac{a}{b} = \frac{c}{d}$
$\frac{a}{b} = \frac{d}{c}$
$\frac{4a}{7b} = \frac{c}{d}$
$\frac{a}{d} = \frac{c}{b}$

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Let's expand both sides of the equation:

Left side: (4a + 7b) (4c – 7d) = 16ac - 28ad + 28bc - 49bd

Right side: (4a – 7b) (4c + 7d) = 16ac + 28ad - 28bc + 49bd

Setting the left side equal to the right side gives us:

16ac - 28ad + 28bc - 49bd = 16ac + 28ad - 28bc + 49bd

Subtracting 16ac, 28bc, and 49bd from both sides gives us:

-28ad = 28ad

Dividing both sides by 28ad gives us:

-1 = 1

This is a contradiction, so the original equation is not possible. Therefore, none of the options are correct.

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