It is known that ax + by = 7, ax's square + by's Square = 49, ax's cube + by's cube = 133, ax's fourth power + by's fourth power = 406 Find the value of 17 (a + b) of 1999 (x + y) + 6xy-2

It is known that ax + by = 7, ax's square + by's Square = 49, ax's cube + by's cube = 133, ax's fourth power + by's fourth power = 406 Find the value of 17 (a + b) of 1999 (x + y) + 6xy-2

Given ax + by = 7, ax ^ 2 + by ^ 2 = 49, ax ^ 3 + by ^ 3 = 133, ax ^ 4 + by ^ 4 = 406, find the value of 1995 (x + y) + 6xy-17 / 2 * (a + b)
Multiply (x + y) on both sides of ax ^ 2 + by ^ 2 = 49 to get
(x+y)(ax^2+by^2)=49(x+y)
Expand to get:
ax^3+bxy^2+ax^2y+by^3=49(x+y)
ax^3+by^3+xy(ax+by)=49(x+y)
133+7xy=49(x+y)
The results are as follows
19+xy=7(x+y)···········①
Multiply (x + y) on both sides of ax ^ 3 + BX ^ 3 = 133 to get
(x+y)(ax^3+by^3)=133(x+y)
ax^4+bxy^3+ax^3y+by^4=133(x+y)
ax^4+by^4+xy(ax^2+by^2)=133(x+y)
406+49xy=133(x+y)
58+7xy=19(x+y)··········②
For the convenience of solving, let x + y = m, xy = n, ①, ② simultaneous equations,
19+n=7m
58+7n=19m
The solution is: M = 5 / 2, n = - 3 / 2,
That is: x + y = 5 / 2, xy = - 3 / 2, from x + y = 5 / 2 get: y = 5 / 2-x, substitute xy = - 3 / 2, get
x(5/2-x)=-3/2
x^2-5/2x-3/2=0
(x+1/2)(x-3)=0
X = - 1 / 2 and 3, corresponding y = 3 and - 1 / 2;
For convenience, if x > y, then
X = 3, y = - 1 / 2, substituting ax + by = 7, ax ^ 2 + by ^ 2 = 49, we get
3a-1/2b=7
9a+1/4b=49
To solve the equations, a = 5, B = 16
therefore
1995(x+y)+6xy-8.5×(a+b)
=1995m+6n-8.5×(a+b)
=1995×5/2+6×(-3/2)-8.5×(5+16)
=4800
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http://zhidao.baidu.com/question/23290862.html?fr=qrl3