Maths Assignment help!!?

[firasjavid]

Pls help me to complete my maths assignment

Signs-
√ = square root
² = square
x¯ = bar ( 0.7¯ = 0.77777777...) (0.47¯¯=0.47474747..)
^ = rasied to power of eg. 4^-2 = 1/16

****** 1. if a = 8+3√7 and b =1/a then find a² +b²

2. Express 0.6 + 0.7¯ + 0.47¯¯ in the form p/q where p and q are integers and q is not equal to 0

3.Rationalise 1 / √ 3 +√ 2 -√ 5

4. Find the value of a and b in √ 7-1 / √ 7+1 - √ 7+1 / √ 7-1 = a +b√ 7

5. If x, y and z are real numbers show that √ x^-1 √y * √y^-1 √z * √z^-1 √x =1

6. (i) a+b =11 , ab =28 find the value of a³ + b³
(ii) if x² + 1/x² =18 find the value of x³ - 1/x³

7. (i) if a+b+c = 5 and ab+bc+ca= 10 , prove that a³ + b³ +c³-3abc = -25
(ii) If a , b , c are all non zero and a+b +c =0 then prove that a²/bc + b²/ca + c²/ab =3

8. Find the value of a and b so the polynomial x³ + 10x² + ax + b is exactly divisible by (x-1) as well as by (x+2) ​

Thanks if u helped i really needed this
if some are confusing just skip it

 

[HallsofIvy]

Pls help me to complete my maths assignment

Signs-
√ = square root
² = square
x¯ = bar ( 0.7¯ = 0.77777777...) (0.47¯¯=0.47474747..)
^ = rasied to power of eg. 4^-2 = 1/16

****** 1. if a = 8+3√7 and b =1/a then find a² +b²

2. Express 0.6 + 0.7¯ + 0.47¯¯ in the form p/q where p and q are integers and q is not equal to 0

3.Rationalise 1 / √ 3 +√ 2 -√ 5

4. Find the value of a and b in √ 7-1 / √ 7+1 - √ 7+1 / √ 7-1 = a +b√ 7

5. If x, y and z are real numbers show that √ x^-1 √y * √y^-1 √z * √z^-1 √x =1

6. (i) a+b =11 , ab =28 find the value of a³ + b³
(ii) if x² + 1/x² =18 find the value of x³ - 1/x³

7. (i) if a+b+c = 5 and ab+bc+ca= 10 , prove that a³ + b³ +c³-3abc = -25
(ii) If a , b , c are all non zero and a+b +c =0 then prove that a²/bc + b²/ca + c²/ab =3

8. Find the value of a and b so the polynomial x³ + 10x² + ax + b is exactly divisible by (x-1) as well as by (x+2)
​

Thanks if u helped i really needed this
if some are confusing just skip it

What, exactly do you mean by "help"? What kind of help do you need? Can you, for example, find \(\displaystyle (2+ 3\sqrt{5})^2\)? What about \(\displaystyle \frac{1}{2+ 3\sqrt{5}}\)?

 

[lookagain]

Pls help me to complete my maths assignment

Signs-
√ = square root
² = square
x¯ = bar ( 0.7¯ = 0.77777777...) (0.47¯¯=0.47474747..)
^ = rasied to power of eg. 4^-2 = 1/16

****** 1. if a = 8+3√7 and b =1/a then find a² +b²

2. Express 0.6 + 0.7¯ + 0.47¯¯ in the form p/q where p and q are integers and q is not equal to 0

3.Rationalise 1 / √ 3 +√ 2 -√ 5

4. Find the value of a and b in √ 7-1 / √ 7+1 - √ 7+1 / √ 7-1 = a +b√ 7

5. If x, y and z are real numbers show that √ x^-1 √y * √y^-1 √z * √z^-1 √x =1

6. (i) a+b =11 , ab =28 find the value of a³ + b³
(ii) if x² + 1/x² =18 find the value of x³ - 1/x³

7. (i) if a+b+c = 5 and ab+bc+ca= 10 , prove that a³ + b³ +c³-3abc = -25
(ii) If a , b , c are all non zero and a+b +c =0 then prove that a²/bc + b²/ca + c²/ab =3

8. Find the value of a and b so the polynomial x³ + 10x² + ax + b is exactly divisible by (x-1) as well as by (x+2) ​

Thanks if u helped i really needed this
if some are confusing just skip it

firasjavid, that is not the way to post on here. I see you're posting advanced algebra/some
level of number theory/advanced math problems.

Post one problem per thread.

The "help" you get is by showing your work here first. For example, you might write
"Here is my work so far on such-and-such problem. Would you help me from this step on?"

Read the (more complete) rules for posting here:

http://www.freemathhelp.com/forum/threads/41536-Read-Before-Posting!!



This isn't a classroom to teach you how to do those problems as if you've never been
exposed to them or to similar ones.

If you were state something like that you don't know how to do them at all, then this
site is not for you, and we are not to spend our time with you as it would be
wasteful.

 

[mmm4444bot]

Pls help me to complete my maths assignment

Help to complete? We cannot complete that which has not yet been started.

Show us what you can do; then we'll be in a position to help you complete it. :cool:

 

[hoosie]

Help with Maths Assignment

Pls help me to complete my maths assignment

Signs-
√ = square root
² = square
x¯ = bar ( 0.7¯ = 0.77777777...) (0.47¯¯=0.47474747..)
^ = rasied to power of eg. 4^-2 = 1/16

****** 1. if a = 8+3√7 and b =1/a then find a² +b²

2. Express 0.6 + 0.7¯ + 0.47¯¯ in the form p/q where p and q are integers and q is not equal to 0

3.Rationalise 1 / √ 3 +√ 2 -√ 5

4. Find the value of a and b in √ 7-1 / √ 7+1 - √ 7+1 / √ 7-1 = a +b√ 7

5. If x, y and z are real numbers show that √ x^-1 √y * √y^-1 √z * √z^-1 √x =1

6. (i) a+b =11 , ab =28 find the value of a³ + b³
(ii) if x² + 1/x² =18 find the value of x³ - 1/x³

7. (i) if a+b+c = 5 and ab+bc+ca= 10 , prove that a³ + b³ +c³-3abc = -25
(ii) If a , b , c are all non zero and a+b +c =0 then prove that a²/bc + b²/ca + c²/ab =3

8. Find the value of a and b so the polynomial x³ + 10x² + ax + b is exactly divisible by (x-1) as well as by (x+2) ​

Thanks if u helped i really needed this
if some are confusing just skip it

Example to help with Question 1 from Maths Assignment
(Question 1 : If a = 8+3√7 and b =1/a then find a² +b²)


EXAMPLE: If a = 5+4√2 and b = 3/a then find a² +b²
a² = (5+4√2)(5+4√2)
Remember (1 + 2)(3 + 4) = 1*3+1*4+2*3+2*4 = 3+4+6+8 = 21
Check: (1 + 2)(3 + 4) = (3)(7) = 21
a² = 5*5+5*4√2+4√2*5+4√2*4√2 ⇒ a² = 5*5+5*4√2+4√2*5+4√2*4√2
⇒ a² = 25+20√2+20√2+16*2 ⇒ a² = 25+40√2+32
⇒ a² = 57+40√2 Since b =3/a it follows b² = (3/a)² = 9/a² ⇒ b² = 9/(57+40√2)
Rationalising the denominator gives:
b² = 9/(57+40√2) * (57-40√2)/(57-40√2) ⇒ b² = 9(57-40√2)/(3249-1600*2)
⇒ b² = 9(57-40√2)/(3249-3200)
⇒ b² = (513-360√2)/49 Therefore a²+b² = 57+40√2+513/49-(360/49)√2
⇒ a²+b² = (3306+1600√2)/49

 

[lookagain]

hoosie, I would recommend you not typing any additional examples for that lazy user.

As Denis already mentioned in this thread, he/she posted at other sites and was supplied
with worked-out solutions for doing nothing.