find the value of a in the following equation (7/12)^a+8 divide (7/12)^-7+4 = (7/12)^2a divide (7/12)^4a+6
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Answer:
( -11 + √73 ) / 2 or ( -11 - √73 ) / 2
Step-by-step explanation:
( 7 / 12 )^a + 8 ( 7 / 12 )^2a
———————— = ————————
( 7 + 12 )^-7 + 4 ( 7 / 12 )^4a + 6
a + 8 2a
=> ——— = ———
-7 + 4 4a + 6
=> ( a + 8 ) ( 4a + 6 ) = 2a × ( -3 )
=> 4a² + 38a + 48 = - 6a
=> 4a² + 38a + 6a + 48 = 0
=> 4a² + 44a + 48 = 0
=> 4 ( a² + 11a + 12 ) = 0
=> a² + 11a +12 = 0
Here a = 1, b = 11, c = 12
a = {-b ± √( b² - 4ac )} / 2a
= { -11 ± √( 11² - 4 × 1 × 12 )} / 2 × 1
= { -11 ± √( 121 - 48 )} / 2
= ( -11 ± √73 ) / 2
= ( -11 + √73 ) / 2 or ( -11 - √73 ) / 2
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