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Root5 /2 root5 -1
can be written in the form
a+rootb /c
where a, b and c are integers.
Find the values of a, b and c when the resulting fraction
is written in its simplest form.

Root5 /2 root5 -1 can be written in the form a+rootb /c where a, b and c are integers. Find the values of a, b and c when the resulting fraction is written in i class=

Answer :

Answer:

10, 5, 19

Step-by-step explanation:

Recall that

[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]

So we can multiply the fraction by

[tex] \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } [/tex]

And get

[tex] \frac{ \sqrt{5} }{2 \sqrt{5} - 1} \times \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } = \frac{10 + \sqrt{5} }{20 - 1} = \frac{10 + \sqrt{5} }{19} [/tex]

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