Question

root 5 minus 1 by root 5 + 1 + root 5 + 1 by root 5 minus 1 is equal to a + b root 5 then find a and b​

Answer 1

Answer:

3

Step-by-step explanation:

$\frac{ \sqrt{5} -1 }{ \sqrt{5} + 1} + \frac{ \sqrt{5} + 1 }{ \sqrt{5} - 1} \\ \\ = \frac{ {( \sqrt{5} - 1) }^{2} }{ (\sqrt{5} + 1)( \sqrt{5} - 1) } + \frac{ {( \sqrt{5} + 1) }^{2} }{ (\sqrt{5} - 1)( \sqrt{5} + 1) } +$

According to the formula,

$(x + y)(x - y) = {x}^{2} - {y}^{2} \\ = \frac{ (\sqrt{5} - 1)^{2} }{ {( \sqrt{5}) }^{2} - {1}^{2} } + \frac{ (\sqrt{5} + 1)^{2} }{ {( \sqrt{5}) }^{2} - {1}^{2} } \\ = \frac{ { (\sqrt{5} )}^{2} - 2 \sqrt{5} + {1}^{2} }{5 - 1} + \frac{ { (\sqrt{5} )}^{2} + 2 \sqrt{5} + {1}^{2} }{5 - 1} \\ = \frac{5 - 2 \sqrt{5} + 1 }{4} + \frac{5 + 2 \sqrt{5} + 1 }{4} \\ = \frac{6 - 2 \sqrt{5} + 6 + 2 \sqrt{5} }{4} \\ = \frac{12}{4} \\ = 3$

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Answer 2

Answer:

Here is Your answer

Step-by-step explanation:

(√5-1)×(√5-1). (√5+1)×(√5+1)

__________. +. __________. = a+b√5

(√5+1)×(√5+1). (√5-1)×(√5+1)

5-2√5+1. 5+2√5+1

_______. +. _______.

5-1. 5-1

6-2√5. 6+2√5

_____. +. _____

4. 4

3-2√5. 3+2√5

______ +. ______

2 2

3-2√5+3+2√5

____________. 【Cross out (-2√5) & (2√5)】

2.

Then,

3+3/2. = 6/2

=3

THANK YOU!