If a -5-1-5-1 and b -5-1-5-1- the value of a 2- ab - b 2- a 2- ab - b 2 is -A- 5 - 3B- 34C- None of theseD- 4 - 3E- 3 - 5

The correct option is D 4/3 Given expression is = ((a+b)^2 ab)/((a b)^2 + ab) Solving we get (4/3) ...

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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 :

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4/3

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3/5

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5/3

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None of these

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Solution

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

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

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

a^{2} + b^{2}

a + b = 5

a b = 3

(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

a + b = 5,

a

b

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