O-Level Additional Math

[red rose]

rylee:

red rose:

Need help to solve this.


x - 2/x + 3 = 2x^2 + x - 10/x^2 + 6x + 9

I only managed to get x = -2, but the answer key says the answer should be x = 2 or x = -2. Please advise.

Thank you in advance.

Hi red rose,

The answer is x=+2 or -2

Working as follow:-

(x-2)/(x+3)=(2x^2+x-10)/(x+3)^2

(x-2)(x+3)=2x^2+x-10

X^2-2x+3x-6=2x^2+x-10
X^2+x-6=2x^2+x-10
x^2-6 =2x^2-10
x^2=4
x=+2 or -2

Regards.

:thankyou: Greatly appreciated!

[jtoh]

Thanks rylee.

[blitz]

URGENT


Need help to solve this.

If X^2+Y^2=8 and (X+Y)=5 Find the value of 4XY

and

Given that (a/3)=Square root of ((b+1)/(b-1))
express b in terms of a
Find b if a=7

Thank you in advance.

[FrekiWang]

blitz:

URGENT


Need help to solve this.

If X^2+Y^2=8 and (X+Y)=5 Find the value of 4XY

and

Given that (a/3)=Square root of ((b+1)/(b-1))
express b in terms of a
Find b if a=7

Thank you in advance.

Both questions are very standard, you may have to revise your work carefully since you have difficulties in them.
1.
X+Y=5
(X+Y)^2=25
X^2+2XY+Y^2=25
given X^2+Y^2=8
2XY=25-8=17
4XY=34
(I do not like the question as X and Y are not real numbers)

2.
Square both sides, we have
a^2 / 9 = (b+1) / (b-1)
Cross multiplying them, we have
(a^2)b - (a^2) = 9b + 9
(a^2 - 9)b = 9 + a^2
b = (9+a^2) / (a^2 - 9)
if a=7,
b=(9+49)/(49-9)=58/40=29/20 (or 1.45)

[blitz]

Thanks FrekiWang

[Andrew Lee]

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

Hi, can help me solve this question:

a. 7(x+3)-(4x-5)=5-(3x+6)

The HCF of two numbers is 1 and the LCM of these numbers is 91, what are the numbers? :roll:

b.(12y-4)/6 = (7y-4)/5

The product of the ages of a group of teenagers (13-19 yr old) is 4590 yrs, Find --
(i) the numbers of teenagers in the group :roll:
(ii) the sum of their ages :roll:

[Andrew Lee]

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

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[HeSheMe]

Andrew Lee:

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

Hi, can help me solve this question:

a. 7(x+3)-(4x-5)=5-(3x+6)

The HCF of two numbers is 1 and the LCM of these numbers is 91, what are the numbers? :roll:

b.(12y-4)/6 = (7y-4)/5

The product of the ages of a group of teenagers (13-19 yr old) is 4590 yrs, Find --
(i) the numbers of teenagers in the group :roll:
(ii) the sum of their ages :roll:

a. 7(x+3)-(4x-5) = 5-(3x+6)
7x+21-(4x-5) = 5-3x-6
7x+21-4x+5 = 5-3x-6
3x+26 = -1-3x
3x+3x = -1-26
6x = -27
x = -27/6

The two numbers are 1 and 91.

Highest common factor = 1
Lowest common multiple = 91 (1x91)

b. (12y-4)/6 = (7y-4)/5
(6y-2)/3 = (7y-4)/5
5(6y-2) = 3(7y-4)
30y-10 = 21y-12
30y-21y = -12+10
9y = -2
y = -2/9

[HappieNewbie123]

Hi,

just curious, what sec one teach? (in maths lah!)

[bluesky63]

hi, can anyone help to solve this question for my daughter, it is o level A Maths question from acs


determine the values of p for which the line y = x - 2p is a tangent to the curve x^2+y^2 = 16p


Thanks