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】Given that x is any number except 2, x ^ 2 + 2x + 1 / (X-2) ^ 3 = A / X-2 + B / (X-2) ^ 2 + C / (X-2) ^ 3, find the value of a, B, C Given that x is any number except 2, x ^ 2 + 2x + 1 / (X-2) ^ 3 = A / X-2 + B / (X-2) ^ 2 + C / (X-2) ^ 3, find the value of a, B, C
By the following conditions:
（x²+2x+1）/（x-2）³=A/（x-2）+B/（x-2）²+C/（x-2）³
Right general score: [a (X-2) & sup2; + B (X-2) + C] / (X-2) & sup3;,
Both sides of the equation have the same denominator and the same numerator,
x²+2x+1=Ax²-4Ax+4A+Bx-2B+C,
x²+2x+1=Ax²-（4A-B）x+（4A-2B+C）
Compare the coefficients
A=1,
-4A+B=2,
4A-2B+C=1,
A = 1, B = 6, C = 9
It is known that a = 2 √ a + 3; b = √ 3a-1; C = 1 / 2 √ 10A (x + 1); where a and B are the simplest quadratic radicals, and a + B = C. find the values of a and X
Note: √ is a radical sign, and the following formulas are all in the root sign
A. B is the simplest quadratic radical
a+3=3a-1
a=2
x=8
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