A few days ago

HikariKawaii

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

Anonymous

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

y = [9 + sqrt(49)]/4 = (9+7)/4 = 4

Therefore,

2^x = 1/2 = 2^(-1)

2^x = 4 = 2²

Thus,

x = -1, x = 2

is the answer.

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