Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 87

6 When one quarter of a number is subtracted from one third of the number, the result is 7. Find the

number.

7 Roses cost$ 5 each and geraniums cost$ 3 each. Michelle bought 4 more geraniums than roses, and

in total she spent$ 52. How many roses did she buy?

8 Nick has 40 coins in his collection, all of which are either 5 -cent or 10 -cent coins. If the total value of

his coins is$3: 15 , how many of each coin type does he have?

9 A store sells batteries in packets of 6 or 10. In stock they have 25 packets which contain a total of 186

batteries. How many of each packet size are in stock?

Equations of the form xn=k where n=2, 3 , 4 , ...... arenotlinear equations. They are in fact called

power equations.

We have already seen that: If x^2 =k where k> 0 , then x=§

p

k.

If we know that the solution has to be positive then x=

p

k.

In general, ² ifnis odd and xn=k, then x=n

p

k

² ifnis even and xn=k where k> 0 , then x=§n

p

k.

Example 17 Self Tutor

Use your calculator to solve forx, giving answers correct to 3 significant figures.

a x^2 =6 b x^2 =13, x> 0 c x^3 =31

a x^2 =6

) x=§

p

6

) x¼§ 2 : 45

b x^2 =13, x> 0

) x=

p

13

) x¼ 3 : 61

c x^3 =31

) x=^3

p

31

) x¼ 3 : 14

See graphics calculator

instructions for finding

cube roots (page 14 ).

Example 18 Self Tutor

Solve forx:

x

2

=

5

x

x

2

=

5

x

fLCD=2xg

)

x£x

2 £x

=

5 £ 2

x£ 2

fto get a common denominatorg

) x^2 =10 fequating numeratorsg

) x=§

p

10

E POWER EQUATIONS

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Y:\HAESE\IGCSE01\IG01_03\087IGCSE01_03.CDR Tuesday, 7 October 2008 12:45:14 PM PETER