some f4 maths

☆ 天與空 ★ ◤

2007-04-21 8:16 am

Consider the graph of y= x^2 - 2x +3 , find the equation of a straight line to be drawn on the graph in order to solve each of the following equations.

(a) 2(x^2) - 2x +1 = 0

(b) -(x^2) + 8x - 7 = 0

p.s. please state the step clearly...

回答 (1)

2007-04-21 8:33 am

✔ 最佳答案

(a) 2x² - 2x + 1 = 0
(2x² - 2x + 1)/2 = 0 /2
x² -x + (1/2) = 0
x² -x + (1/2) - x + ( 5/2) = 0 -x + (5/2)
x² -2x + 3 = -x + (5/2)
therefore, x is the solution of the following equations:
y = x² -2x + 3
y = - x + (5/2)

the equation of straight line to be drawn is : y = - x + (5/2)

(b) -x² + 8x - 7 = 0
x² - 8x + 7 = 0
x² - 8x + 7 + 6x -4 = 0 + 6x -4
x² - 2x + 3 = 6x - 4

therefore, x is the solution of the following equations:
y = x² - 2x + 3
y = 6x - 4

the equation of straight line to be drawn is : y = 6x - 4

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