Urgent Maths help needed (2 Viewers)

[marcquelle]

Hey guys can you help me out with some questions the ones in green are top priority ( so can you help me with these first) then the blue


a)Factorise Completely 8x^4 – 64x
b)Simplify √48 - √27 +√3
c)If x=2^2 and y=3^4,express 4^6x27^8 in terns of x and y.
d)Solve the quadratic equation x – 8x – 9 = 0 by completing the square. Give your answer in exact form.
e)…. | 3^x for x > 2
f(x)| √4-x^2 for -2≤x≤2
… .∟-(2+x) for x < -2
f)The roots of the quadratic equation 4x^2 + 9x + 5=0
i) α+β
ii) α β
iii) α ^-1 + β^-1
iv) α^2 β + αβ^2
g)Simplify Cos^2 A Tan2 A + Cos^2 A

(can you please show working)

Thank You in advanced
Marcquelle

 

[blackglitter]

b) √48 - √27 +√3
= 4√3 - 3√3 + √3
= 2√3

 

[kaz1]

f)

i) -b/a=-9/4
ii)c/a=5/4

The rest of the questions are too confusing too read.

 

[lyounamu]

Hey guys can you help me out with some questions the ones in green are top priority ( so can you help me with these first) then the blue



a)Factorise Completely 8x4 – 64x
b)Simplify √48 - √27 +√3
c)If x=22 and y=34,express 46x278 in terns of x and y.
d)Solve the quadratic equation x – 8x – 9 = 0 by completing the square. Give your answer in exact form.
e)…. �* 3x for x > 2
f(x)| √4-x2 for -2≤x≤2
… .∟-(2+x) for x < -2
f)The roots of the quadratic equation 4x2 + 9x + 5=0
i) α+β
ii) α β
iii) α -1 + β-1
iv) α2β + αβ2
g)Simplify Cos^2 A Tan2 A + Cos^2 A

(can you please show working)

Thank You in advanced
Marcquelle

I cannot see question e) very well...and is the second one supposed to be in absolute value or what?

f) alpha + beta = -b/a = -9/4
alpha x beta = c/a = 5/4
alpha - 1 + beta - 1 = -9/4 - 2 = -17/4 Or are they in power of -1? They are too confusing to read. Please fix...
is iv) supposed to have power there or just times it by two?

 

[marcquelle]

yeah sorry guys i have fixed it all up now sorz

 

[lyounamu]

yeah sorry guys i have fixed it all up now sorz

You sure? What about the polynomial ones? Are they in power or what? If they aren't in power, you can easily do it by yourself because it's just simple multiplication.

 

[kaz1]

d)Solve the quadratic equation x – 8x – 9 = 0 by completing the square. Give your answer in exact form.

Assuming x² – 8x – 9 = 0
x² – 8x + (-4)² -16-9=0
(x-4)²-25=0
(x-4)²=25
(x-4)=(+-)5
x=-1,9

 

[jellybelly59]

d) x^2 -8x -9 =0
x^2-8x+16-16-9 = 0
(x-4)^2 = 25
x = (+-)5+4
x = -9 and 1

 

[Finx]

b)Simplify √48 - √27 +√3

√48 = √16x√3 = 4√3
√27 = √9x√3 = 3√3

so 4√3-3√3+√3 = 2√3

d)Solve the quadratic equation x – 8x – 9 = 0 by completing the square. Give your answer in exact form.
[[I think you mean x²]]

x² - 8x - 9 = 0
x² - 8x = 9 (add 9 to both sides)
x² - 8x + 16 = 25 (add 16 to both sides, I got 16 by dividing the middle term, 8, by two, then squaring it)
(x - 4)² = 25 (factorising LHS)
x - 4 = √25 (rooting both sides)
x - 4 = +/- 5
x = 4 +/- 5 (adding 4 to both sides)
x = 9, -1

e)…. �* 3x for x > 2
f(x)| √4-x2 for -2≤x≤2
… .∟-(2+x) for x < -2

This is for sketching a function, I assume? Draw y=3x, y=√4-x² and y=-x-2 on the same number plane. Then rub out the bits that don't appear in each condition respectively. (Try dividing the number plane into three horizontal sections, with imaginary lines at x=2 and x=-2).

f)The roots of the quadratic equation 4x2 + 9x + 5=0
i) α+β
ii) α β
iii) α -1 + β-1
iv) α2β + αβ2

First, factorise.
4x² + 9x + 5 = 0
(4x+5)(x+1) = 0
.'. x = -5/4, -1
α = -5/4
β = -1


a) is already explained, I'm not sure about c), and I can't be bothered with g) at the moment, soz =[

 

[Bainesy]

d)Solve the quadratic equation x – 8x – 9 = 0 by completing the square. Give your answer in exact form.

Assuming x² – 8x – 9 = 0
x² – 8x + (-4)² -16-9=0
(x-4)²-25=0
(x-4)²=25
(x-4)=+-5
x=1,-9

Ummm, you can jump straight from x² – 8x – 9 = 0

to (x+1)(x-9) = 0

hence x=-1,9

 

[bored of sc]

(a) I think you mean 8x⁴ - 64x.

If so:

8x (x³ - 8) < --- Common factor of 8x taken out.
= 8x (x-2) (x² + 2x + 4) <--- Factorise cubic part using the difference of 2 cubes.

(b) √48 - √27 + √3
= √(16x3) - √(9x3) + √3
= 4√3 - 3√3 + √3
= 2√3

(d) x² - 8x - 9 = 0
x² - 8x = 9
x² - 8x + 16 = 9 + 16
(x-4)² = 25
x-4 = + 5
x = 9, x = -1

(g) cos²A . tan²A + cos²A
= cos²A . sin²A/cos²A + cos²A
= sin²A + cos²A
= 1

 

[Aplus]

f)The roots of the quadratic equation 4x2 + 9x + 5=0
i) α+β
ii) α β
iii) α -1 + β-1
iv) α2β + αβ2

First, factorise.
4x² + 9x + 5 = 0
(4x+5)(x+1) = 0
.'. x = -5/4, -1
α = -5/4
β = -1

I personally wouldn't do that. You should use the rules for sum of roots.

 

[bored of sc]

Ummm, you can jump straight from x² – 8x – 9 = 0

to (x+1)(x-9) = 0

hence x=-1,9

But it says solve by completing the square. I guess you could do it that way to check if you are right.

 

[kaz1]

Ummm, you can jump straight from x² – 8x – 9 = 0

to (x+1)(x-9) = 0

hence x=-1,9

Ummm, it said to solve using completing the square.

 

[Finx]

Ummm, you can jump straight from x² – 8x – 9 = 0

to (x+1)(x-9) = 0

hence x=-1,9

If you read the question, it says to solve by completing the square.

 

[lyounamu]

I personally wouldn't do that. You should use the rules for sum of roots.

Um...that doesn't really matter (unless the question specifically tells you to use that method). In many of the questions, you will sometimes find that this way of method is better. But if the question is hard to factorise and everything, it's best to go with what you suggested there.

 

[ratcher0071]

d) x^2 -8x -9 =0
x^2-8x+16-16-9 = 0
(x-4)^2 = 25
x = (+-)5+4
x = -9 and 1

x = -5+4
x = -1

or

x = 5+4
x = 9

 

[marcquelle]

thanks so much guys i really appreciate this

e) ….* 3^x for x > 2
f(x)| √4-x^2 for -2≤x≤2
….∟ -(2+x) for x < -2

would
3^x for x > 2 be expotential component?
√4-x^2 for -2≤x≤2 be semi-circle component?
-(2+x) for x < -2 be a straight line component?

 

[jellybelly59]

x = -5+4
x = -1

or

x = 5+4
x = 9

oh shit! LOL my bad hahaha sorry im kind of out it

 

[Finx]

thanks so much guys i really appreciate this

e) ….�* 3^x for x > 2
f(x)| √4-x^2 for -2≤x≤2
….∟ -(2+x) for x < -2

would
3^x for x > 2 be expotential component?
√4-x^2 for -2≤x≤2 be semi-circle component?
-(2+x) for x < -2 be a straight line component?

Yuppp. Well done.