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Quantitative Aptitude

Equations

If a =√5+1/√5...

Question

If $a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} a n d b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}, t h e v a l u e o f (\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}})$ is :

A

34

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B

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C

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D

None of these

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Solution

The correct option is B

Given expression is = ((a+b) $^{2}$ -ab)/((a-b) $^{2}$ + ab)

Solving we get (4/3)

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Similar questions

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

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

, then the value of

\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}

Q. Find the value of

a^{2} + b^{2}

a + b = 5

a b = 3

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{[1 - {(\frac{a}{b})}^{- 2}] a^{2}}{(\sqrt{a} - \sqrt{b})^{2} + 2 \sqrt{a b}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ = 1

a + b = 5,

a

b

(a + b) : (a - b) = 1 : 5

(a^{2} - b^{2}) : (a^{2} + b^{2}) .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{[1 - {(\frac{a}{b})}^{- 2}] a^{2}}{{(\sqrt{a} - \sqrt{b})}^{2} + 2 \sqrt{a b}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ =

1 and a + b = 5, then find a and b respectively.

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