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Question
Evaluate the following using identities:
117 x 83
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Solution
The given expression is 117 x 83
We have
`(117 + 83)/2 = 200/2`
= 100
So we can express 117 and 83 in the terms of 100 as
117 = 100 + 17
83 = 100 - 17
117 x 83 = (100 + 17)(100 - 17)
We shall use the identity `(x - y)(x + y) = x^2 - y^2`
Here
(x + y) = 100 + 17
(x - y) = 100 - 17
By applying in identity we get
`(100 + 17)(100 - 17) = (100)^2 - (17)^2`
= 10000 - 289
= 9711
Hence the value of 1117 x 83 is 9711
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