maths help

"express the following in the form a+b root 5, where a and b are constants"
how do i apply this question to these 4 questions...
(2+root5)squared
(3-2root5)squared
1 over root 5 + 1
1+ root 5 over 2- root 5
ASAP

Reply 1

usycool1

19

Original post by caitlindavies

"express the following in the form a+b root 5, where a and b are constants"
how do i apply this question to these 4 questions...
(2+root5)squared
(3-2root5)squared
1 over root 5 + 1
1+ root 5 over 2- root 5
ASAP

What have you done/tried so far?

You need to expand the first two and rationalise the denominator for the last two.

(edited 8 years ago)

Reply 2

caitlindavies

OP

Original post by usycool1

What have you done/tried so far?

You need to expand the first two and rationalise the denominator for the last two.

i havent done anything so far, i just dont understand what it means by a and b are constants

Reply 3

usycool1

19

Original post by caitlindavies

i havent done anything so far, i just dont understand what it means by a and b are constants

a and b are constants (i.e. non changing values, basically a number in each case) that you need to work out.

Reply 4

davros

16

Original post by caitlindavies

i havent done anything so far, i just dont understand what it means by a and b are constants

It means that whatever you work out the answer to be in each case, it will look like

a + b\sqrt{5}

where a and b are some 'ordinary' numbers (not surds) that you have to work out for yourself.

Reply 5

DFranklin

18

Original post by caitlindavies

i havent done anything so far, i just dont understand what it means by a and b are constants

Concrete example (which is intentionally not one of the expressions you've been asked to find):

To express

\dfrac{1}{3-\sqrt{5}}

in the form

a + b \sqrt{5}

:

\dfrac{1}{3-\sqrt{5}} = \dfrac{1}{3-\sqrt{5}} \dfrac{3+\sqrt{5}}{3+\sqrt{5}} = \dfrac{3+\sqrt{5}}{(3-\sqrt{5})(3+\sqrt{5})} = \dfrac{3+\sqrt{5}}{3^2 - \sqrt{5}^2}

(treating the denominator as the difference of 2 squares)

= \dfrac{3+\sqrt{5}}{9 - 5} = \dfrac{3+\sqrt{5}}{4} = \dfrac{3}{4} + \dfrac{1}{4}\sqrt{5}

(This answers the question, with a = 3/4 and b = 1/4, but you don't actually need to state what a and b would be).

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