SOLUTION: IF [(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0] FIND THE VALUE OF X....please help me to solve this problem..as soon as possible...Thank you

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Question 1133750: IF [(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0] FIND THE VALUE OF X....please help me to solve this problem..as soon as possible...Thank you
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

first expand:








...factor
...group




Real solution:

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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

IF [(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0] FIND THE VALUE OF X....please help me to solve this problem..as soon as possible...Thank you
This problem is EXTREMELY easy......easier than you would ever think.
You'll notice that the variable here is actually the binomial X - 4. SO, let X - 4 be a
Then becomes: .
Now, using the RATIONAL ROOT THEOREM, LONG DIVISION of POLYNOMIALS, or SYNTHETIC DIVISION, and the factors of 6. which are 1, -1, 2, -2, 3, -3, 6, or -6,
we find that: , and so, 6 is a ROOT of the function: .
Since X - 4 = a, and a = 6, we can say that: X - 4 = 6, and so:
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