f.4 maths(我要長細答案同解釋)

1) 2x-3y=2......(1)
x^2+y^2+3x-2=0......(2)
由(1) , x = (3y+2)/2 , 代入(2) :
[(3y+2)/2]^2 + y^2 + 3(3y+2)/2 - 2 = 0
[(3y+2)^2] / 4 + y^2 + (9y+6)/2 - 2 = 0
(3y+2)^2 + 4y^2 + 2(9y+6) - 8 = 0
9y^2 + 12y + 4 + 4y^2 + 18y + 12 - 8 = 0
13y^2 + 30y + 8 = 0
(13y + 4)(y + 2) = 0
y = - 4/13 or y = - 2
x = [3(-4/13) + 2]/2 = 7/13 or x = [3(-2) + 2]/2 = - 2
(x = 7/13 , y = - 4/13) or (x = - 2 , y = - 2)

2) -3x+4y=x^2+y^2=25
由-3x + 4y = 25 , 得 y = (3x+25)/4 , 代入x^2+y^2=25 :
x^2 + [(3x+25)^2] / 16 = 25
16x^2 + 9x^2 + 150x + 625 = 400
25x^2 + 150x + 225 = 0
x^2 + 6x + 9 = 0
(x + 3)^2 = 0
x = - 3 , y = (3*(-3)+25)/4 = 4



3)他們歲數的平方和是936 :
x^2 + y^2 = 936......(1)
六年後,父親的歲數會是女兒的歲數的3倍 :
x + 6 = 3(y + 6)......(2)
由(2) : x = 3y + 12 = 3(y+4) , 代入(1) :
9(y+4)^2 + y^2 = 936
9(y^2 + 8y + 16) + y^2 - 936 = 0
10y^2 + 72y - 792 = 0
5y^2 + 36y - 396 = 0
(5y + 66)(y - 6) = 0
y = - 66/5(捨去) or y = 6
x = 3*6+12 = 30
父現時30歲
女現時 6 歲