1 Answer

Tardomatic · Answer 1 · 2021-09-10T03:45:31+0000

Answer:

x=-4.37 or 1.37

Explanation:

The equation whose solution is to be found is;

$1 + (3)/(x)= \frac{6}{ {x}^(2) }$

we now multiply through by

${x}^(2)$

This implies that;

$( {x}^(2))1 +({x}^(2) * (3)/(x))= {x}^(2) * \frac{6}{ {x}^(2) }$

$\implies{x}^(2)+3x=6$

Subtracting - 6 from both side we obtain;

${x}^(2) + 3x - 6 = 6 - 6$

$\implies{x}^(2) + 3x - 6 =0$ We now obtain a quadratic equation.So, let us use quadratic formula to find the solutions.

Comparing the equation ,

${x}^(2) + 3x - 6 = 0$

to the general quadratic formula,

$a {x}^(2) + bx + c = 0$

we can say that,

a=1,b=3 and c=-6

putting this in to the quadratic formula,

$\implies x = \frac{ -b\pm \sqrt{{b}^(2) - 4ac} }{2a}$ , we obtain

$x = \frac{-3\pm \sqrt{ {3}^(2) - 4(1)(-6)} }{2(1)}$

Simplifying we obtain,

$x = ( -3\pm √(9+24))/(2)$

$\implies x = (-3-√(33) )/(2)or (-3+√(33))/(2)$

x=-4.37 or 1.37

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