F4 math problem~!!－gbu94mz95e的部落格

標題:

F4 math problem~!!

發問:

The height x (cm) of afather is more than 3 times the height y (cm) of his baby son by 10 cm. If the height of the father were 36 cm more,while the height of his baby were 36 cm less, then the father's height will be equal to the square of that of his baby son.(a) Write down the equations connecting x and... 顯示更多 The height x (cm) of afather is more than 3 times the height y (cm) of his baby son by 10 cm. If the height of the father were 36 cm more,while the height of his baby were 36 cm less, then the father's height will be equal to the square of that of his baby son. (a) Write down the equations connecting x and y. (b) Solve the equations and find the heights of the father and his son.

最佳解答:

(a) The height x (cm) of afather is more than 3 times the height y (cm) of his baby son by 10 cm => x = 3y + 10 If the height of the father were 36 cm more,while the height of his baby were 36 cm less, then the father's height will be equal to the square of that of his baby son => x+36 = (y-36)2 So x = 3y + 10 and x = y2 - 72y + 1260 (b) Put x = 3y + 10 into x = y2 - 72y + 1260 3y+10 = y2 - 72y + 1260 y2 - 75y + 1250 = 0 (y-50)(y-25) = 0 y = 50 or y = 25 If y = 50, x = 3y + 10 = 160 If y = 25, x = 85 Since the height of the baby is more than 36cm from the second condition, the solution pair y = 25 and x = 85 is rejected. So x = 160, y = 50. The heights of the father and his son are 160cm and 50cm, respectively.

其他解答:

x=3y+10....(1) x+36=(y-36)^2....(2) (1)代入(2)....(3y+10)+36=(y-36)^2 3y+46=y^2-2(y)(36)+36^2 3y+46=y^2-72y+1296 y^2-72y+1296-3y+46=0 y^2-75y+1342=0 y=29.48434或45.51560