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Algebra and Applications Test 2

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Question : 16 of 40

Marks: +1, -0

What are the values of A and B respectively, if

\frac{\sqrt{5}-1}{\sqrt{5}+1}+\frac{\sqrt{5}+1}{\sqrt{5}-1}=A+B\sqrt{5}

3, 0
0, 3
0, 0
3, 3
None of these

Solution: 👈: Video Solution

Concept:

Rationalize each radical denominator, then simplify and compare with

A+B\sqrt{5}

.

Explanation:

\frac{\sqrt{5}-1}{\sqrt{5}+1}=\frac{(\sqrt{5}-1)^2}{(\sqrt{5}+1)(\sqrt{5}-1)}=\frac{5+1-2\sqrt{5}}{5-1}=\frac{6-2\sqrt{5}}{4}

.

\frac{\sqrt{5}+1}{\sqrt{5}-1}=\frac{(\sqrt{5}+1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)}=\frac{5+1+2\sqrt{5}}{5-1}=\frac{6+2\sqrt{5}}{4}

.

Adding them gives

\frac{6-2\sqrt{5}+6+2\sqrt{5}}{4}=\frac{12}{4}=3

.

So

A+B\sqrt{5}=3=3+0\sqrt{5}

.

Thus

A=3

and

B=0

.

Answer:

A=3

,

B=0

; option A.

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