Question

(Root5 -1/root 5+1)+(root 5+1/roots-1)=a+b root 5

Answer 1

Answer:

hope the answer is correct

Answer 2

Answer:

The value of a = 3, b = 0.

Step-by-step explanation:

Given,

(Root5 -1/root 5+1)+(root 5+1/roots-1)=a+b root 5

Writing in mathematical form

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

To find,

The values of 'a', and 'b'

Calculation,

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

Considering the L.H.S

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

$\frac{((\sqrt{5})^2+1^2 -2\sqrt{5})+((\sqrt{5})^2)+1^2+2\sqrt{5})}{(\sqrt{5})^2-1^2}\\ \implies \frac{5 +1 +5 +1}{5 -1} \\\implies \frac{12}{4} \\\implies L.HS = 3$

Hence, 3 = a + b√5

⇒ 3 + 0(√5) = a + b√5

a = 3, b = 0

therefore, the value of a = 3, b = 0.

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