f ( x ) = ( x + 2) ( x - 2) + ax + b
If f ( 2 ) = 2 and f ( -2) = 4
find the vaules of a and b
數學題= =
2007-12-26 8:09 pm
回答 (2)
2007-12-26 8:22 pm
✔ 最佳答案
(2+2)(2-2)+2a+b=2(-2+2)(-2-2)+(-2a)+b = 4
2a+b=2
-2a+b=4
b=2-2a
b=4+2a
2-2a=4+2a
2-4=4a
a= -0.5
b=2-2(-0.5)
b=3
Hence, a= -0.5 and b=3
2007-12-27 11:27 pm
f ( x ) = ( x + 2) ( x - 2) + ax + b
--------------------------------------------------------------
f ( 2 ) = ( 2 + 2) ( 2 - 2) + 2a + b
f ( 2 ) = 2a + b = 2
f ( 2 ) = 2
2a + b =2
b = 2 - 2a ---------------(1)
--------------------------------------------------------------
f ( -2 ) = ( -2 + 2)( -2 - 2) - 2a + b
f ( -2 ) = b - 2a
f ( -2 ) = 4
b - 2a = 4 ---------------(2)
put (1) into (2)
b - 2a = 4
2 - 2a - 2a = 4
-4a = 2
a = -1/2
So,
b = 2 - 2a
b = 2 - 2(-1/2)
b = 3
--------------------------------------------------------------
f ( 2 ) = ( 2 + 2) ( 2 - 2) + 2a + b
f ( 2 ) = 2a + b = 2
f ( 2 ) = 2
2a + b =2
b = 2 - 2a ---------------(1)
--------------------------------------------------------------
f ( -2 ) = ( -2 + 2)( -2 - 2) - 2a + b
f ( -2 ) = b - 2a
f ( -2 ) = 4
b - 2a = 4 ---------------(2)
put (1) into (2)
b - 2a = 4
2 - 2a - 2a = 4
-4a = 2
a = -1/2
So,
b = 2 - 2a
b = 2 - 2(-1/2)
b = 3
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