A few days ago
Add maths need help badly!!?
2^(2x-1) -9 * 2^(x-2) + 1 = 0
Substitution
Can you please explain it to me?
Top 2 Answers
A few days ago
Favorite Answer
2^(2x-1) -9 * 2^(x-2) + 1 = 0
<=> 2^(2x)*2^(-1) – 9*2^(x)*2^(-2) + 1 = 0
<=> (1/2) (2^x)² – (9/4) 2^x + 1 = 0
Substituting y = 2^x, we get a quadratic equation w.r.t. y:
(1/2) y² – (9/4)y + 1 = 0
Multiplying both sides by 4, we obtain:
2y² – 9y + 4 = 0
Use the quadratic formula to find solitions, taking into account that y cannot be negative:
discriminant = (-9)² – 4(2)(4)
= 81 – 32 = 49
y = [9 – sqrt(49)]/4 = (9-7)/4 = 1/2
or
y = [9 + sqrt(49)]/4 = (9+7)/4 = 4
Therefore,
2^x = 1/2 = 2^(-1)
or
2^x = 4 = 2²
Thus,
x = -1, x = 2
is the answer.
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A few days ago
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