1970-02-17 — Page 22

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170英文中學會考試題預習專欄

報日僑華

二期星日七十月二年〇七九一曆公年九十五國民華中

育教僑

Note: Where there are only two square roots in the equation, as in the given example, it is advisable

have one square root on one side of the equation

and the other square root on the other side.

The given equation is thus writsen

+ 2) = ? ~/√(x + 9):

Squaring 2 + 2 = 49 - 14√(2 + 9} + x + 9)

−56 = −14 √√(x + +(x+9) |

9)

Squating again: 16:

x+9

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This value for x will be found to check in the original equation and hence the required solution

數學科

(十六)

1 x 7.

Example

Solve 47 21-1

MATHEMATICS (13)

13英文中學會考試題預習專欄

英文科

道英文書院主編

(十六)

ENGLISH LANGUAGE (16)

Answers to Exercise 15

13.

25.

14.

26.

15%

27.

16.

28.

17.0

29.

18. (D)

30.

19.

31.

-20.

32.

9. 10%.

21.

33.

22.

34.

11. 12. (0)

·23%

24.

Solution of Equations

Special Quadratic Equations Certain equations which do not appear to be of the quadratic types can often be reduced to this form by means of a substitution as in the following examples.

Example 1′′ Solve z 3 + 2 -.

Letz u and the given equation becomes the quadratic equation

– 3a + 2 = 0

(u − 1)(u − 2)

oz 2

Divide all numerators, resp. by their denominators

Then (6 + - - g ) + (2 ♦ — — - ) - (3 + — — 5 )

(5+ ===)

= - -

8) (x

(x − 5) (x − 7)

c2 2

Exazole 2 fölve vír

If sly 1) be replaced

the equation Decomes

from (1)

2.or

(1)

(2)

0

or

From (2)

-3

2

-12x + 32

12x+35

The equality holds under the condition that the numeratore nàould equal to zero,

Example 6- Solve ~(z2 - 3x + 6) − y(x2 - 3x + 3) - It is to be noted that is -3x occurs in both

of the quantities under the square root signs, and

replacing this by p the equation can be written.

√(x + 6) = √(p + 3) ×

√(p + 6) = 1 +√(D + 3)

Squaring this equation

P + 6 = 1 + 2 (p + 3)

1.3. 2 - 2 No(p + 3)

Squaring again,

-&L.H.S.

Pracia

Sha great link that binds all parts of the British empire together is the possession of a coMMON literature and a common language. A common religion, a DDAEON Justsprudence, and common traditions have not united the peoples of Western Europe - France, Spain, and Italye tha sasential link is wanting, He haar of Shakespeare being acted and Skakaupaare scoiaties being formed in our mous äletant colonias. å spiritual link is thus forged, strongar than any political links could be, These Epirit of a great genius moves upon the fros of the waters that divide the remote colonies from the notherland

Whatever may be the fate of the empire, va faal sure that the radcstal of Shakespears will stand. Ho do not feel guile the same confidënoe about his greatest osadenssparies, - Bacon, Ben Jenson, or nam Posteat speedzzare, – Kilton, Wordswarth, Tennyson.

What then de toe secret of Shakespeare'i influence? Fettäs originality of his plots; for all his plots (with me single exception) are borrowed; - not the remodelling of the English dramas: for this was the work of Kazlowe, who wrote plays of a high order before Shakespeare did; - not the introduotion of blank vezse as the metre of dialogues för this had been done alzandy; — not the depth of his learning; for he consalted translations whenever he could, in prefazendo te the originals, and many of his class: oa) allusions are wrong. (Has geography is sometimas at fault. Es gives Bohemia a Bea-oosst, and makes Kilen

seaport.)

The main secret of his influence lies in bLE humanity, - kis extra-ordinary susceptibility to every phase of human feeling in all ranks of life, hia prodigious, faculty of assimilation, his power of identifying himself with the pharacters that he pourtrays. This was the genius born in hinta #203Lár genius, thengk not of so wide a range, was born in Dickens. He enters into the terrible remorse, yet stern unvielding courage, of Macbeth, as truly as into the humble giety of Henry VI. Nothing that pertained to man was alien to this universal spirit. He has Mell bean callad "ghe thousand-souled Shakes nasza."

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Hence, the complete solution is

Equations-davolving Square Roots When dealing with the equation x = 3, if it be squared the result is

- 9 from which the solutions are z • + 3. Thus it can be soon that if a given equation be squared there is a possibility of introducing a value for the variable which does not actually satisfy the original squation and must be discarded as being an extraneous root introduced by squaring.

Honos, when dealing with aquations which are solved by means of squaring, the roots obtained mua T always be tested in the original equation and any value that does not satisfy the original equation must be discarded,

Examples, veive the equation

2 √(x + 1) -

-3√√(2x-

-5)=√(x − 2).

Squaring the given equation

4(x+1)-12;{ [(x+1)(2x+5)] + 9(2x-5)

3.6. 4x+4–12^/ ( 2x2-3x-5)

21x – 39 – 12°

7x

18x

• 12 √(272

3x-5)

-13-4√(2x2

Squaring again

49x-182*

*

169 = 16 (2x2 3x

H.S.

Simultanesas Linsaz Equations

The mathod of solution or u iséɛpendent squations in i ujkkowna, as show in the exa

in to eliminate the variables one by one until an saviation in only one variable is obtained.

Solve the equations

·(1) (2)

275

24

−10 ± √(100 – 4)

-10 ± √96

14 ..... (3)

IT IN GIGar”from Ubo équations that it is isst to eliminate the variable s first:

Substituting these values of y in (3)

·3(-5 ± √6)

-376 +216

1 + 15 + 6/6

316

216

(b) Two hemogeneous quadratic expressions squal to

a constant to form two equations.

(3) - (2)

Ex

(2) x (2)

6x +

(5) - (1)

\(5) - (4)

Using - 1 in (4)

Hence the solution As

(4) 4212 ...

•(5)

Exempla

folvatne equations

ུས་

1341 + 249 M. 0.

1.8. (17z - 83)(≈ − 3) ·

블루

Uning x = 1 in the original equation

2 N( 12 + 1) − 37/(316 - s)

3/20 - 3/

20

√(37 - 2) -√(22) - J17

Therefore I -

does not satisfy the original.

aquation and must be discarded as an extraneous foot.

Using 3

Simultaneous quadratic EquationE

(a) One liseer and one quadratic equat).on

From the linear equation find the value of one of the variables in terms of the other and rubešitute this in the quadratie aquation, the obtaining a quadratic equation in a single variable from which two values of that variable. can be obtained.

Solve the aquationa

From wat. (2)

L.■.S. - 2√4

RES. Wi

Substituting for x from (3) in (1)

therefore the solution 18 x=

2(1

Example

solve the equation√√(x+2) + √√(x+9)

3(1

|:+ &y(1 − 37)

(2) x 2

(1)

Sxy

Ey or 2y

By substitut

67 in (2)

(1) (2)

- 3

in (2)

(3)

2

Hence the complete solution in

(3)