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7^9+9^7 is divisible by (A) 16 (B) 24 (C...

`7^9+9^7` is divisible by (A) 16 (B) 24 (C) 64 (D) 72

Text Solution

Verified by Experts

The correct Answer is:
1
Given expression `= 7^(9) + 9^(7) = (1 + 8)^(7) - (1 - 8)^(9)`
`= (.^(7)C_(0) + .^(7)C_(1) 8 + .^(7)C_(2) 8^(2) + ... + .^(7)C_(7) 8^(7) - (.^(9)C_(0) - .^(9)C_(1) 8 + .^(9)C_(2) 8^(2) .... - .^(9)C_(9) 8^(9))`
`= (1 + 7 xx 21 xx 8^(2) + ...) - (1 - 9 xx 8 + 36 xx 8^(2) + .... - 8^(9))`
`= ( 7 xx 8 + 9 xx 8) + (21 xx 8^(2) - 36 xx 8^(2)) +`....
`= 2 xx 64 + (21 - 36) 64 +`.....
Which is divisible by 64
Hence, the statement is true
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