If 49a^2 + 30ab + 25b^2 - 100ab = 289 then what is the value of (2187)^a/(243)^b = ?

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01 Oct 2020 Find the value of

If 49a^2 + 30ab + 25b^2 - 100ab = 289
then what is the value of (2187)^a/(243)^b = ?

OPtion

1) 903981141
2) 387420489
3) 043046721
4) 129140163
5) 903961141
6) 387460489
7) 043049721
8) 129180163
9) 387120489
10) None of these

Solution

49a^2 + 30ab + 25b^2 - 100ab = 289
=> 49a^2 -70ab +25b^2 =289
=> (7a-5b) ^ 2 = 289
=> 7a - 5b = 17

2187^a/243^b = 3^(7a) / 3^(5b) = 3^(7a-5b)
Now, 7a - 5b = 17

=> so 3^(7a-5b) = 3^17 = 129140163
Option 4)

Correct Option: 4 Best Solution (1)