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题 两抛物线 ｙ2 =7-3ｘ与ｘ2 =7-3 ｙ在第一象限内交点的个数为 ( )(Ａ) 1 (Ｂ) 2 (Ｃ) 3 (Ｄ) 4解 考查两抛物线 ｙ2 =7-3ｘ ,ｘ2 =7-3 ｙ可知它们关于直线 ｙ =ｘ对称 ,以 ｙ =ｘ代入方程 ｙ2 =7-3ｘ ,得ｘ2 +3ｘ -7=0 ,解得ｘ =-3± 3 72 ;以ｘ =ｙ代入
The number of intersections of the two parabola y2 = 7-3x and x2 = 7-3 y in the first quadrant is () (A) 1 (B) 2 (C) 3 (D) 4 Solution Two parabolas y2 = 7 -3x,x2 =7-3 y, we know that they are symmetric about the straight line y = x, and y = x is substituted into the equation y2 = 7-3x. We get x2 +3x -7=0 and the solution is x =-3± 3 72; x = y substitution