中四中五數學題幾問－貨運百科

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中四中五數學題幾問

發問:

6.factorize y4[y4次方]-13y[13y2次方]2+36 7.solve the simultaneos equations: 2x-y=5 x2[x2次方]+xy=2 13.solve the simultaneos equations: x+y=3 3x[3的x次方]+3y[3的y次方]=12

最佳解答:

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6. Let x = y2y4 - 13y2 + 36= x2 - 13x + 36= (x - 9)(x - 4)= (y2 - 9)(y2 - 4)= (y + 3)(y - 3)(y + 2)(y - 2)= (y - 3)(y - 2)(y + 2)(y + 3)7. 2x - y = 5 ─── (1)x2 + xy = 2 ─── (2)From (1): y = 2x - 5 ─── (3)Put (3) into (2):x2 + x(2x - 5) = 2 3x2 - 5x - 2 = 0 (3x + 1)(x - 2) = 0 x = 2 or -1/3 When x = 2, y = 2(2) - 5 = -1 When x = -1/3, y = 2(-1/3) - 5 = -17/3 13. x + y = 3 ─── (a) 3x + 3y = 12 ─── (b) From (a): y = 3 - x ─── (c) Sub (c) into (a): 3x + 33 - x = 12 3x + 33/3x = 12 32x + 27 = 123x (3x)2 - 123x + 27 = 0 (3x - 9)(3x - 3) = 0 3x = 9 or 3 x = 2 or 1 When x = 2, y = 1 When x = 1, y = 2

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