HELP plz! (1 Viewer)

[ahohen_77]

Here are some ext questions in the 3 unit cambridge text book which i couldnt get:

1.if (a+b)^2 + (b+c)^2 + (c+d)^2=4(ab+bc+cd), prove that a=b=c=d

2.factorise A^4 +B^4. - in the answers it sez that this equals (A^2-ABsqrt2+B^@)(A^2+ABsqrt2+B^2)

3.Simplify
1/(a-b)(a-c) + 1/(b-c)(b-a) + 1/(c-a)(c-b)

Thanks

 

[Grey Council]

hrm, you look as if your in year 11. ^_^ well, trust me, get your algebra SHARP!

anyway, i'll quickly do the second one.
btw, the question, unless i'm mistaken, is:
factorise A⁴ +4B⁴
just check. I'll do it without the 4 though.

a^4 + b^4
= (a^2 + b^2)^2 - 2(a^2)(b^2)
= (a^2 + b^2)^2 - ((2^1/2)ab)^2
taking difference of two squares:
(a^2 - ab.sqrt2 + b^2)(a^2 + ab.sqrt2 + b^2)
as required.
hope that helped.

 

[CM_Tutor]

Question 1: Expand, cancel the common ab, bc and cd terms, and you should be able to refactorise it to
(a - b)² + (b - c)² + (c - d)² = 0. Since each of these terms is zero or positive (for a, b, c and d real), and they sum to zero, each must be 0.

Thus, a - b = 0, b - c = 0, and c - d = 0, and so a = b, b = c, c = d, or more simply, a = b = c = d

Question 3: You need a common denominator, so you need the terms in the same form. I left the first term alone, rewrote the second as (-1) / [(b - c) * (-1) * (b - a) = -1 / (b - c)(a - b), and rewrote the third as
[(-1) * (-1)] / [(-1) * (c - b) * (-1) * (c - a)] = 1 / (b - c)(a - c). I then took a common denominator of
(a - b)(a - c)(b - c), and simplified to get the answer 0.

 

[ahohen_77]

thanks guys!