As maths urgent help please?!?!

a. = ( (1+√5)/2 )²
= (1+2√5+5)/4
= (6+2√5)/4
= (3+√5)/2
= (2+1+√5)/2
= (2/2) + ( (1+√5)/2 )
= 1+y

Thank you soon much it all makes sense !!

Any ideas on part b ?

Very grateful for a) thanks

If y = (1+ sqrt5)/2, then 1/y = 2/(1+sqrt5)

Then you have to rationalise the bottom

Thanks
But I got 1/y = (2root5)/5 ?! 😳

Thanks
But I got 1/y = (2root5)/5 ?! 😳

When you find the reciprocal of a number, you basically just flip it upside down. So if

y=(1+sqrt5)/2, then to find 1/y you just flip this fraction, hence

1/y = 2/(1+sqrt5)

Then you should know that to rationalise the bottom, you multiply top and bottom by the conjugate of the bottom (the same thing, but with the sign in the middle changed). In this case, the conjugate would be 1-sqrt5

This is the working for part b

Posted from TSR Mobile

Okay I tried working it out :

2 * (1-sqrt5) =. 2-2sqrt5

(1+sqrt5) * (1-sqrt5) = -4

So I ended up getting
(2-2sqrt5)/-4

Argh ! I'm not understanding this but I'm glad your helping because the beginning makes sense

People - have you read the maths forum rules? Full solutions are not helpful and shouldn't be posted - just give a hint.

Sorry, I have understood there working out now I've learnt from that and have several other questions similar to those to work out.

you're spot on so far! You can take a common factor of 2 out of the top and divide it, which leaves you with:

(1-sqrt5)/-2

Little tip here, is that you can divide the minus 1 into the top by changing all the signs on the top:

(1-sqrt5)/-2 = (sqrt5 - 1)/2

Now you need to use a little bit of imagination. We want to have y in our answer, and we know y=(1+sqrt5)/2, so we need that term. Think of a clever way to add 0 to our equation, that will give you the solution they want