中三數學題

1) 3^-2a = 9^3a
3^-2a = (3^2)^3a
3^-2a = 3^6a
-2a = 6a
-2a - 6a = 0
-8a = 0
a = 0
2) 4^x + 1 - 2^x = 3
4^x +1 - 2^x = 3
(2^2)^x - 2^x = 3 - 1
(2^x)(2^x) - 2^x = 2
2^x (2^x - 1) = 2

let 2^x = X
X(X - 1) = 2
X^2 - X - 2 = 0
(X - 2)(X + 1) = 0
X = 2, -1

Therefore, 2^x = 2, -1
(i) When 2^x = 2,
x = 1
(ii) When 2^x = -1,
no solution

Therefore, x = 1

1.2





2.41

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