If a, B, x, y satisfy ax + by = 3, ax + by = 7, ax + by = 16, the fourth power of AX + the fourth power of by = 42, find the value of the fifth power of AX + the fifth power of by

If a, B, x, y satisfy ax + by = 3, ax + by = 7, ax + by = 16, the fourth power of AX + the fourth power of by = 42, find the value of the fifth power of AX + the fifth power of by

Let f (n) = ax ^ n + by ^ n, x, y be T ^ 2 = Pt + Q, then x + y = P, xy = - Q. P (AX + by) + Q (AX + by) = (x + y) (AX + by) - XY (ax + by) = ax + by, that is, ax + by = P (AX + by) + Q (AX + by), f (3) = PF (2) + QF (1)
Ax + BX = 3, ax ^ 2 + by ^ 2 = 7, ax ^ 3 + by ^ 3 = 16, ax ^ 4 + by ^ 4 = 42, find ax ^ 5 + BX ^ 5
Ax ^ 2 + by ^ 2 = 7 (AX ^ 2 + by ^ 2) (x + y) = 7 (x + y) ax ^ 3 + by ^ 3 + ax ^ 2Y + bxy ^ 2 = 7 (x + y) ax ^ 3 + by ^ 3 + XY (AX + by) = 7 (x + y) substitute ax + by = 3, ax ^ 3 + by ^ 3 = 16 into the above equation 16 + 3xy = 7 (x + y) ax ^ 3 + by ^ 3 = 16 (AX ^ 3 + by ^ 3) (x + y) = 16 (x + y) ax ^
If the real numbers a, B, X and y satisfy ax + by = 3 and ay BX = 5, then the value of (A2 + B2) (x2 + Y2) is______ .
From the meaning of the question, ax + by = 3 & nbsp; & nbsp; & nbsp; & nbsp; ① ay BX = 5 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ② ① 2 is a2x2 + b2y2 + 2abxy = 9 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ③ ② 2 is a2y2 + b2x2-2abxy = 25 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ④
Let a = {x | X's square-8x + 15 = 0}, B = {x | AX-1 = 0}, if B is contained in a, find the set of real numbers a~
I already know the answer, but I don't understand why we need another a = 0, so the B set is empty~
B is contained in a
Then B can be an empty set
It must be noted that when B is a subset of a, we must not forget the empty set
Empty set means that the equation has no solution
So the coefficient of X is 0
So a = 0