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急! F5 About equations 1exq03

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16. (a) 2x+ y = 5 ...... [1] x +y2 = 10 ...... [2] (b) [2]*2 : 2x + 2y2 = 20 ...... [3] [3] - [1] : 2y2 - y = 15 2y2 - y - 15 = 0 (2x + 5)(y - 3) = 0 x = -5/2(rejected) or y = 3 Put y = 3 into [1] : 2x + 3 = 5 x = 1 Hence, x =1 and y =3 17. Let d be the denominator of the original fraction. (7 + 2)/(d + 2) = (7/d) + (1/20) [9/(d + 2)] - (7/d) = 1/20 [9d - 7(d + 2)]/[d(d + 2)] = 1/20 20(2d - 14) = d(d + 2) 40d - 280 = d2 + 2d d2 - 38d + 280 = 0 (d - 10)(d - 28) = 0 d = 10 or d = 28(rejected) The original fraction = 7/10 18. (a) Width of the original rectangle = 224/x cm Width of the new rectangle = (224/x) + 1 cm (x - 1)[(224/x) + 1] - 224 = 1 (x - 1)(224 + x)/x = 225 x2 + 223x - 224 = 225x x2 - 2x - 224 = 0 (x - 16)(x + 14) = 0 x = 16 or x = -14(rejected) Hence, x = 16

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