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Question

If "from the square of a half the sum of two numbers we subtract the square of a half their difference the result is the:

A
sum of the two numbers
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B
quotient of the two numbers
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C
difference of the two numbers
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D
product of the two numbers
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Solution

The correct option is B product of the two numbers
Let two number x and y.
Now sum of these two numbers = x+y
Now Half of these two number = x+y2
Now square will be = (x+y2)2
Now if we subtract x and y and than half of these numbers will be xy2
Square will be (xy2)2
Now subtracting
(x+y2)2(xy2)2
x2+2xy+y24x22xy+y24
x2+2xy+y2x2+2xyy24
4xy4=xy
Hence it will be the product of the two numbers

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