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Question

If x2 + y2 = z2. Then which of the following is/are true?


A

2 = 1 +

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B

2 = 1 +

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C

2 = 1 +

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D

2 = 1 +

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Solution

The correct options are
A

2 = 1 +


B

2 = 1 +


Given x2 + y2 = z2

x2 = z2 - y2

x2 = (z-y) (z+y)

Taking logarithms on both sides on base (z+y) and (z-y) respectively.

We get,

2logy+zx2 = logy+z(y+z) + logy+z(zy)

2logy+zx = 1 + logy+z(zy)

logzyx2 = logzy(zy) + logzy(y+z) (Taking log with base (z-y))

2logzyx = 1 + logzy(y+z)


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