Cambridge International Mathematics

Example 6 Self Tutor

Solve 2 x=4¡x by graphing y=2x and y=4¡x on the same set of axes.

Give your answer correct to 3 significant figures.

Let Y 1 =2x and Y 2 =4¡x

Using a graphics calculator, we find that they meet

when x¼ 1 : 39.

) the solution is x¼ 1 : 39

Example 7 Self Tutor

Solve 2 x=4¡x by drawing one graph. Give your answer correct to 3 significant figures.

2 x=4¡x

) 2 x¡4+x=0

We graph y=2x¡4+x using a graphics

calculator to help.

Thex-intercept is¼ 1 : 39

) x¼ 1 : 39

EXERCISE 23C.2

1 Use technology to solve:

a ¡ 2 x^2 =x¡ 3 b^12 x^2 =x+2 c x(x¡2) = 3¡x

d (x+ 2)(x¡1) = 2¡ 3 x e (2x+1)^2 =3¡x f (x¡2)^2 =1+x

2 UsingMethod 1to solve, correct to 3 significant figures:

a 2 x= b

p

x=3¡x c x^2 =

p

x+2

d 3 x=5 efx^3 +2=3x¡x^2

3 UseMethod 2to solve, correct to 3 significant figures:

a x^3 ¡x+3=0 b 5 ¡x=

p

x c 3 x=x^3 +1

d x^2 ¡3=^3

p

x e 3 x^2 +1=

12

x¡ 4

f

x+7

x¡ 3

=2¡x

4 Find the coordinates of the points, correct to 2 decimal places, where these graphs meet:

a y=x^2 +2x¡ 3 and y=

4

x

b y=x^3 and y=5x

c y=

5

x

and y=

1

p

x

+1 d y=2x¡ 1 and y=

1

x^3

3 x

3 x=x^2

Further functions (Chapter 23) 479

IGCSE01

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Y:\HAESE\IGCSE01\IG01_23\479IGCSE01_23.CDR Tuesday, 11 November 2008 10:49:29 AM PETER