Question

Solution of the equation $= \frac{1}{4}\left( \frac{3}{8}x + \frac{3}{4} \right)\left( 1 + \frac{x^{2}}{4} \right)^{- 1} + \frac{5}{8}\frac{1}{( - 2)}\left( 1 - \frac{x}{2} \right)^{- 1}$are.

• A. 0
• B. 6
• C. 4
• D. None of these

Answer 1

Answer: (B)

6

Answer 2

$= 20^{- 2\log_{20}(1/9)} = 20^{2\log_{20}9} = 20^{\log_{20}9^{2}} = 9^{2} = 81\lbrack\log_{b}a.\log_{c}a - \log_{a}a\rbrack + \lbrack\log_{a}b.\log_{c}b - \log_{b}b\rbrack + \lbrack\log_{a}c\log_{b}c - \log_{c}c\rbrack = 0$

$x = \frac{9}{4}$ $\frac{1}{\ln a.\ln b.\ln c}\lbrack(\ln a)^{3} + (\ln b)^{3} + (\ln c)^{3} - 3\ln a.\ln b.\ln c\rbrack = 0$

$\Rightarrow$ $\ln a + \ln b + \ln c = 0$ $\ln(abc)$ $\lbrack a^{3} + b^{3} + c^{3} - 3abc = 0$ $a + b + c = 0\rbrack$ $\therefore$

This value satisfies the given equation.

$abc = 1$.