RARY
育教僑華頁三第張六第 2
日九十月正年戌庚曆夏 WAH KIU YAT PO 日橋
郭日僑華
24LB 1970
二期星日四廿月二年〇七九一曆公年九十五國民藥 中
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(接第六張第二頁)
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Example 3. Oblaine the value of
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(+b)
MATHEMATICS (17)
the Theory of Indices.
We are familiar with the following laws
(1)
(111)
(iv)
(vi£) *1/* . *~
Example 1 Simplify and express with positiva
(a)
·
{a2 + b2 + •b)(a? + o# - ot) {at_b#+0#) (b*+o2¬a*)
[(a*+b*).
Exp. - (a*b*) + o*] (a+b) _ot] [o++ (at_bt)]
Tot
-[(at + b2)2 - 0] [a~ (at - bt)?]
(using the difference of two aquaras)
a*b*] [ 2a*b*→ (a+b=0)|
((a+ba)
--2bø - 20a)
2k6+ 2ea + 2ab
Surds and Square Roots of Surds
Sura is usually used to denote an expression
involving, where a is not a perfect ath power
a
of rational number. Thus 2 + √√3, √2 + 3√4, √5 − 2/7. 3/8 + 7/8 ie not a surd as it can
3/2 are surda, but be simplified to 2 + 3 m 5+
26.
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His uztinely coming
quite annoyed.
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(IE)
all our plan. We felt
(A) would destroy (B) had destroyed
(C) was destroying (D) had been destroying. (E) has destroyed
he is not small, he is a coward.
(A) In spite of (B) In oase (C) Provided that
Admitting that (B) However,
he felt, he tried to ëmile to those who greeted him.
(A) Good am (B) As painful as
(C) So broken-hearted (D) Painful as (E) that sorry
де нав
28. He went on working without any stop.
very tired,
in spits of (9) in case (0) provided that notwithstanding that (3) no matter how
When calculating a number such as value of No3 from tables, it is advisable to multiply both numerator and denominator by 3 giving 43
using tas
30.
This method is known as rationalising the denominator;
If/ & +^/h represent a surdic quantity, then bis known as its conjugate murd, and the. product of the two is (a - b) which is a rational number
aber providing a and b are rational.
When simplifying a fraction involving a Burdic denominator, it is necessary to multiply numerator and denominater by the conjugate surd of the denominator, thus obtaining a rational denominator.
(0) 0.42 ± 0.125
(4)-√(23) +
Solution
(a): Exp
g/2n+2n(2n−1)] : 5 [(n+3)+(3n-3)+(−4x)]
Szample 4
Rationalise (s)-1
(b) Exp.
52
− (√2 + 1)
- (2 + 2 √√ 2 + 1 )
√5 + √2 + 2 - 1 √5 + √ 2 + 1)(2+2, 2)
2√2
4 - (2√2)2
10+ 4√2
- 1 √10 +√5 + 2√2 + 3J
3
ta bravery, the whole city would have.
bosa captured by the eneży,
(4) If not for (B) Unless (0) without (D) But fer (F) But that
7 then the people will praise him.
Does he replies wisely
(3) Whether he replies wisely,
(C) If he replies wisely
However he replies wisely
How wisely does he reply
Uneasy lies the head that wears a crown, The Bentence means that
(A) to wear a crown is not easy
(B) to lie down is not easy
(C) a brown is expensive.
(D) to bela leader is not aaay
(E) to wear the valuable jewels makes one
uncomfortable. ·
He makes no friend, who never made a foe. The sentence seans that
(A) a quarrelsome can never sakés friends (B) we should not make enemies.
(C) we should not make our friends become.
it is sometimes unavoidable to make enemy (3); a man without friend usual makes. enemy
Can two walk together arcept they be agreed? The sentence zgana that
(A), it is impossible for two men to walk
together.
(B) two people cannot be together if they walk
too much
two people will not come together unloun they are of the same opinion
(D) two persons should not walk togebar ir they
want to be friends,
every
Give every man thy ear, but few thy voice.
The sentenes means that =
(A) we must not listen to the others
(B) we must not speak to the others
we abenld the other way but
should not speak much.
(D) we should listen to the others and then
disouss, with them
35. The newa wan a dagger to his heart. This means !
that
(a) the news was joyous
(B) the new broke his heart
(C) "the-news confuled his mind
he could not understand the xavs
(e) Exp.-0.4° ± 0.125
- ( 4 )2 = ( } ) } ÷ ( }
( } } ) ( 1 ) ( } )
(4) xxp. - (2),*) * (- ̄ }, }) (_,-1,}
J-11, 11-8
#
prove that.
(5-2)2 (√3 + 2)(√5
(15 - 2)(5
5-45-13.45 - 18
Fxample 5 Simplify (a
.242 +
- 6.2 + 12√5 – 3.10 −10/10 + 8/5-40/√2 + 20.
31
20/5 - 13.10
Example 6 Find the square roots of (a) 17 + 12/2 (b) 22 12/2
(a)
2 - √2 -√5
3,
(2-3) (4-22/5+ No25) (2+\/5)(4−2,√5 + √25,
ཝཏིརིཏ ཙ ཙ ཝིཏནཱ ཨཝཾ དྷཱི5 +Z Vཀ5 - 5
+(1/5)
3-8/5 + 4 1/25
+5
8 3/5 + 42/25
.13
Squaring 17+
Hence 17 X-
6√2
- 72
Solving sets (1) & (2)
(a) Lot 17 + 12√2
√x + √x
27
(1)
(2).
- 9 y
3+ 2/2
aquaring 22 - 12/2 = x + y
22 = x + y
6/2-√37 1.0. 72 -
())
(2).
From (2) y.
12
(17+ 12√2) 9 + √8
(b) Lat (22–12\/2) =w= −√x
(0)
2-22. 2-2-3
(2−2√2 +/√5) (2+/2 +/5). [2_{√/2+√5)] [2+(√2 +15)]
2√√3 + 2√2 − 4-
(2 + 5 + 2/10)
(~ ~ √a2 = 1)3
x2 - (x + √o2-1)2 + (• - √ a2 - 13°
2(3x) (a2
23+ 6(2
2014 3)
5 - 2/2 + 4/5 -10
(3 + 2/10)
(5-2√2 + 4:√5 −10)(3 — 2/10)
(3 + 2/10)(3 - 2/10)
- 6,2 + 12.√5 – 3.10–10,10 + 4.20 – 8,50+20 |
40)
Using this in eqt (1)
But
22 = x. +
- 22x + 72 = 0.
18)(z
4 or 18
18 or 4
x 18 and
Hence (22 - 12/2) 18