6^(2x-3)+6^x-42=0...

Question

6^(2x-3)+6^x-42=0...

Answer 1

6^х = а ; а > 0
1/( 6^3 )•а^2 + а - 42 = 0
1/216а^2 + а - 42 = 0
а^2 + 216а - 9072 = 0
D = 46656 + 36288 = 82944 = 288^2
a1 = ( - 216 + 288 ) : 2 = 36
a2 = ( - 216 -288 ) : 2 = - 252 ( < 0 )
6 ^ x = 36
6 ^ x = 6 ^ 2
X = 2
Ответ 2