Quadratic & Surds Maths Help

[acroviak]

Hey

Questions as follow.
1. (a) Given that (2+√7)(4-√7) = a + b√7 , where a and b are integers, find the values of a and b.

Im guessing this is simultaneous equations, not sure how to derive them thought :/..

(b) Given that (2+√7)/(4+√7) = c + d√7 , where c and d are rational numbers, find the values of c and d

2. Given that (5-√3)/(1+√3) = a + b√3 where a and b are integers, find the values of a and b.


thats all, thank you very much for any help.

i will check back soon and give best answer to the best answerer :D.

thankee.

[dr b]

try multiplying out the expression and then simplifying (collecting terms involving sqrt(7))

[TCL-MUMPING]

Replace √7 wi Z to give

(2 +Z)(4-Z) = (2 x 4) + (4 x Z) � (2 x Z) - Z^2

Now, knowing that Z^2 is (√7x√7) which equals 7, gives

8 +4Z -2Z -7 or

8 + 2Z-7 or

1 +2Z

Replace the Z wi √7 and you have

1 + 2√7

So a=1 and b=2

Carry out a similar process wi the other two and Robert is yir mither's brither!!!!