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
If (4a + 7b) (4c – 7d) = (4a – 7b) (4c + 7d), then which one of the following is correct?
Options
Solution
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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