Question

(2x +1³) + (x + 2³)/(2x + 1³) - ( x + 2³)=189/61​

Answer 1

Answer:  x = 0.1  and  x = 8.9

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Step-by-step explanation:

$(2x+1^{3} )+\frac{(x+2^{3})}{(2x+1^{3}) } -(x+2^{3} )=\frac{189}{61}$

$(2x+1 )+\frac{(x+8)}{(2x+1) } -(x+8)=\frac{189}{61} \\\\(2x+1)+(x+8)[\frac{1}{(2x+1)} -1]=\frac{189}{61} \\\\(2x+1)+(x+8)[\frac{1-2x-1}{(2x+1)}]=\frac{189}{61}\\\\(2x+1)+(x+8)[\frac{-2x}{(2x+1)}]=\frac{189}{61}\\\\\frac{(2x+1)^{2}-2x^{2} -16x }{(2x+1)} =\frac{189}{61}\\\\\frac{4x^{2}+1+4x-2x^{2} -16x }{(2x+1)} =\frac{189}{61}\\\\\frac{2x^{2}+1 -12x }{(2x+1)} =\frac{189}{61}\\\\61(2x^{2}+1-12x)=189(2x+1)\\\\122x^{2} +61-732x=378x+189\\\\122x^{2} -1110x-128=0\\\\61x^{2} -555x-64=0$

we know that , roots of quadratic equation are :

$x=\frac{-b+\sqrt{b^{2}-4.a.c } }{2.a}$     and    $x=\frac{-b-\sqrt{b^{2} -4.a.c} }{2.a}$

$x=\frac{555-\sqrt{(555)^{2}-4.61.64 } }{2.61}$    and  $x=\frac{555+\sqrt{(555)^{2}-4.61.64 } }{2.61}$

$x=\frac{555-\sqrt{292409 } }{122}$     and     $x=\frac{555+\sqrt{292409 } }{122}$

$x=\frac{555-540.7 }{122}$       and     $x=\frac{555+540.7 }{122}$

x = 0.1  and  x = 8.9