SOLUTION: Find x, 3333²ˣ + 3333⁴ˣ = 11112222

Question 1207342: Find x,
3333²ˣ + 3333⁴ˣ = 11112222
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.
Find x, 3333²ˣ + 3333⁴ˣ = 11112222.
~~~~~~~~~~~~~~~~~~~~~~

Let y =  be new variable. Then the given equation takes the form

    y^2 + y = 11112222.


Simplify and find y

    y^2 + y - 11112222 = 0.


Use the quadratic formula

    y =  = .


Since y =   is positive, we accept the positive root 

    x =  = 3333

and discard the negative root.


So,   = 3333;  hence,  2x = 1  and  x= 1/2 = 0.5.


ANSWER.  x = 1/2 = 0.5.

Solved.

RELATED QUESTIONS
3333/4 (answered by jim_thompson5910)

find the remainder when 3^3x33^33x333^333x3333^3333 is divided by... (answered by ikleyn)

Find the general formula for the sum of this series: 3+33+333+3333+... to n terms (answered by Edwin McCravy)

3+33+333+3333+......+333333333333 in this addition which digit is there at the hundreds... (answered by Edwin McCravy)

A school has 3333 lockers. The first student opens up every single locker. The second... (answered by jim_thompson5910)

Question 3 To find the number of toys a company should manufacturer per day to... (answered by ikleyn)

The probability that a house in an urban area will be burglarized is 55%. If 3333... (answered by ikleyn)

Biologists tagged 98 tagged fish in a lake on January 1. On February 1, they... (answered by ikleyn)

How would one answer this: List all of the number sets that apply to each number.... (answered by CubeyThePenguin)