Answer:
The solutions to the original equation are x = -1 and x = 3.
Step-by-step explanation:
2^2x+1 = 17*2^x - 8
2*2^2x = 17*2^x - 8
To solve the equation 2 * 2^(2x) = 17 * 2^x - 8, let's substitute 2^x with y:
2 * y^2 = 17y - 8
Now, let's factorize this equation:
2y^2 - 17y + 8 = 0
We can factorize this quadratic equation as:
(2y - 1)(y - 8) = 0
Setting each factor equal to zero gives us two possible solutions:
2y - 1 = 0 --> 2y = 1 --> y = 1/2
y - 8 = 0 --> y = 8
Since we substituted y with 2^x, we substitute back to solve for x:
For y = 1/2:
2^x = 1/2
x = -1
For y = 8:
2^x = 8
x = 3
Therefore, the solutions to the original equation are x = -1 and x = 3.
Thanks
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Verified answer
Answer:
The solutions to the original equation are x = -1 and x = 3.
Step-by-step explanation:
2^2x+1 = 17*2^x - 8
2*2^2x = 17*2^x - 8
To solve the equation 2 * 2^(2x) = 17 * 2^x - 8, let's substitute 2^x with y:
2 * y^2 = 17y - 8
Now, let's factorize this equation:
2y^2 - 17y + 8 = 0
We can factorize this quadratic equation as:
(2y - 1)(y - 8) = 0
(2y - 1)(y - 8) = 0
Setting each factor equal to zero gives us two possible solutions:
2y - 1 = 0 --> 2y = 1 --> y = 1/2
y - 8 = 0 --> y = 8
Since we substituted y with 2^x, we substitute back to solve for x:
For y = 1/2:
2^x = 1/2
x = -1
For y = 8:
2^x = 8
x = 3
Therefore, the solutions to the original equation are x = -1 and x = 3.
Thanks