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標題:

a math

發問:

Given that the equations 2x^2+ax-b=0 and 2x^2-bx+a=0 have a common root. find the common rootand the value of a-b. Show steo plz

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• 我有好多題a-maths 唔識
• 台北, 九份, 清境5 天行程@1@
• Agnes b 有冇出過...@1@

 

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Let α be the common root, so (1): 2α^2 +aα -b=0 (2): 2α^2 -bα +a=0 (1)-(2): (a+b)α -b -a = 0 ........ (a+b)α -(a+b) = 0 ................ (a+b) α = a+b ........................ α = 1 Therefore, the common root is 1. i.e., for the x = 1 in (1) 2 (1)^2 + a(1) -b = 0 ................ 2 +a -b = 0 ...................... a-b = -2 Therefore, the value of a-b is -2.

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