Question

find the value of A and B root 5 minus 1 upon root 5 + 1 is equal to a minus b root 5
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Answer 1

Given:

$\star \: \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1 } = a - b \sqrt{5}$

To find :

• The value of a and b .

Solution:

$\implies \: \frac{ \sqrt{5} - 1 }{ \sqrt{5} + 1}$

•Rationalise the denominator :

$\implies \: \frac{ \sqrt{5} - 1 }{ \sqrt{5} + 1 } \times \frac{ \sqrt{5} - 1 }{ \sqrt{5} - 1} \\ \\ \implies \: \frac{ {( \sqrt{5} - 1)}^{2} }{( { \sqrt{5}) }^{2} - {(1)}^{2} } \\ \\ \implies \: \frac{5 + 1 - 2 \sqrt{5} }{5 - 1} \\ \\ \implies \frac{6 - 2 \sqrt{5} }{4} \\ \\ \implies \: \frac{3 - \sqrt{5} }{4} \\ \\ \implies \: \frac{3}{4} - \frac{ \sqrt{5} }{4}$

Now , compare with a-b√5 we get ,

• a = 3/4

and

• b = 1/4.

Formula used :

$\star \: \bold{ {x}^{2} - {y}^{2} = (x + y)(x - y)} \\ \\ \star \bold{{(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}$

Answer 2

Answer:

My name is Radhika. I'm from Kolkata

You are from?