If x1, x2 x3 are the three real solutions of the equation x log 102 x+ log 10 x3+3=(2/(1)√x+1-1-(1)√x+1+1 where x1x2x3, then

Question

If x1, x2 x3 are the three real solutions of the equation x log 102 x+ log 10 x3+3=(2/(1)√x+1-1-(1)√x+1+1 where x1>x2>x3, then (A) x1+x3=2 x2 (B) x 1 ⋅ x 3= x 2 2 (C) x2=(2 x1 x2/x1+x2) (D) x1-1+x2-1=x3-1

Tardigrade Admin · Accepted Answer

RHS when simplified is equal x x1=1 ; x2=(1/10) ; x3=(1/100) log 10 x2 ln =1 sin =0 ; x=1

Q. If $x_{1}, x_{2} & x_{3}$ are the three real solutions of the equation $x^{l o g_{10}^{2} x + l o g_{10} x^{3} + 3} = \frac{2}{\frac{1}{x + 1 - 1} - \frac{1}{x + 1 + 1}}$ where $x_{1} > x_{2} > x_{3}$ , then

$x_{1} + x_{3} = 2 x_{2}$

$x_{1} \cdot x_{3} = x_{2}^{2}$

$x_{2} = \frac{2 x _{1} x _{2}}{x _{1} + x _{2}}$

$x_{1}^{- 1} + x_{2}^{- 1} = x_{3}^{- 1}$

RHS when simplified is equal $x$
$x_{1} = 1; x_{2} = \frac{1}{10}; x_{3} = \frac{1}{100}$
$lo g_{10} x^{2} ln = 1 sin = 0; x = 1$

Q. If x1​,x2​&x3​ are the three real solutions of the equation xlog102​x+log10​x3+3=x+1​−11​−x+1​+11​2​ where x1​>x2​>x3​, then

x1​+x3​=2x2​

x1​⋅x3​=x2​2

x2​=x1​+x2​2x1​x2​​

x1−1​+x2−1​=x3−1​