Solve the above quadratic equation
Attachments:
Answers
Answered by
1
Please mark as brainliest
Attachments:
Answered by
1
Answer:
x = 1 , 2
Solution:
Here,
The given equation is ;
4^(x-1) - 3•2^(x-1) + 2 = 0
The given equation can be rewritten as ;
=> (2²)^(x-1) - 3•2^(x-1) + 2 = 0
=> [2^(x-1)]² - 3•2^(x-1) + 2 = 0
Putting 2^(x-1) = y , the above equation will be reduced to ;
=> y² - 3y + 2 = 0
=> y² - 2y - y + 2 = 0
=> y(y - 2) - (y - 2) = 0
=> (y - 2)(y - 1) = 0
=> y = 1 , 2
Case(1) : If y = 1
=> y = 1
=> 2^(x-1) = 1
=> 2^(x-1) = 2^0
=> x - 1 = 0
=> x = 1
Case(2) : If y = 2
=> y = 2
=> 2^(x-1) = 2^1
=> x - 1 = 1
=> x = 1 + 1
=> x = 2
Hence,
The required answer is ;
x = 1 , 2
Similar questions