If 4+354−35=a+b5, then (a,b)=

4+3.54−3.5=a+b.5=(4+3.5)(4+3.5)(4)2−(3.5)2=16+45+24.516−45=61+24.5−29=−6129+−24295(a,b)=−6129,−2429

If 4+354−35=a+b5, then (a,b)=

4+3.54−3.5=a+b.5=(4+3.5)(4+3.5)(4)2−(3.5)2=16+45+24.516−45=61+24.5−29=−6129+−24295(a,b)=−6129,−2429

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If $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$ , then $(a, b) =$

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$(\frac{61}{29}, \frac{- 24}{29})$

$(\frac{- 61}{29}, \frac{24}{29})$

$(\frac{61}{29}, \frac{24}{29})$

$(\frac{- 61}{29}, \frac{- 24}{29})$

answer is D.

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Detailed Solution

$\frac{4 + 3. \sqrt{5}}{4 - 3. \sqrt{5}} = a + b . \sqrt{5}$

$= \frac{(4 + 3. \sqrt{5}) (4 + 3. \sqrt{5})}{{(4)}^{2} - {(3. \sqrt{5})}^{2}}$

$= \frac{16 + 45 + 24. \sqrt{5}}{16 - 45} = \frac{61 + 24. \sqrt{5}}{- 29}$

$= \frac{- 61}{29} + (\frac{- 24}{29}) \sqrt{5}$

$(a, b) = (\frac{- 61}{29}, \frac{- 24}{29})$

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If $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$ , then $(a, b) =$