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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
%28X-4%29%5E5+-7%28X-4%29%5E4+%2B7%28X-4%29%5E3+-7%28X-4%29%5E2+%2B7%28X-4%29-6=0
first expand:


%28X-4%29%5E3=%28X-4%29%28X-4%29%28X-4%29=X%5E3+-+12+X%5E2+%2B+48+X+-+64
%28X-4%29%5E2=X%5E2-8x%2B16




X%5E5+-+27X%5E4+%2B+279+X%5E3+-+1403X%5E2+%2B+3471+X+-+3410=0...factor
...group


%28X+-+10%29+%28X%5E4+-+17X%5E3+%2B+109+X%5E2+-+313+X+%2B+341%29+=+0

Real solution: X+=10

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Answer by MathTherapy(10552) About Me  (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: matrix%281%2C3%2C+a%5E5+-7a%5E4+%2B+7a%5E3+-+7a%5E2+%2B+7a+-+6%2C+%22=%22%2C+0%29. 

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: matrix%281%2C3%2C+a%5E5+-7a%5E4+%2B+7a%5E3+-+7a%5E2+%2B+7a+-+6%2C+%22=%22%2C+0%29. 

Since X - 4 = a, and a = 6, we can say that: X - 4 = 6, and so: highlight_green%28matrix%281%2C5%2C+X%2C+%22=%22%2C+6+%2B+4%2C+%22=%22%2C+10%29%29