If α, β are the roots of the equation x2−5+3log3⁡5−5log5⁡3x+33log3⁡513−5log5⁡323−1=0 then the equation, whose roots are α+1β and β+1α,

# If  are the roots of the equation ${\mathrm{x}}^{2}-\left(5+{3}^{\sqrt{{\mathrm{log}}_{3}5}}-{5}^{\sqrt{{\mathrm{log}}_{5}3}}\right)x+3\left({3}^{{\left({\mathrm{log}}_{3}5\right)}^{\frac{1}{3}}}-{5}^{{\left({\mathrm{log}}_{5}3\right)}^{\frac{2}{3}}}-1\right)=0$ then the equation, whose roots are ,

1. A

3x2 – 20x – 12 = 0

2. B

3x2 – 10x – 4 = 0

3. C

3x2 – 10x + 2 = 0

4. D

3x2 – 20x + 16 = 0

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### Solution:

Bonus because ‘x’ is missing the correct will be,

So, equation is x2 – 5x – 3 = 0 and roots are

New roots are

Let

As ${\mathrm{\alpha }}^{2}-5\mathrm{\alpha }-3=0$

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