Question

solve using factorisation method

6/x=1+x

(quadratic equation)​

Answer 1

Answer:

$\huge{\underline{\mathfrak{Answer:}}}$

$\textbf{\huge{\underline{Solution:}}}$

$\frac{6}{x} = 1 + x \\Or \: \: \: 6 = x(1 + x) \\ Or \: \: 6 = x + x {}^{2} \\ Or \: \: \: x + x {}^{2} = 6 \\ Or \: \: \: x {}^{2} + x - 6 = 0 \\ Or \: \: \: x {}^{2} + 3x - 2x - 6 = 0 \\ Or \: \: \: x(x + 3) - 2(x + 3) = 0 \\ Or \: \: \: (x + 3)(x - 2) = 0 \\ Or \: \: \: x + 3 = 0 \\ So \: \: \: x = - 3 \\ Again \: \: \: x - 2 = 0 \\ So \: \: \: x = 2 \\ \\ So \: \: \: x = - 3 \: \: \: Or \: \: \: x = 2$

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Answer 2

Answer:

x=-3 or x=2

Step-by-step explanation:

6/x=1+x

1+x=6/x

x=6/x-1

x2=6-x

x2(3-2)x-6=0

x2+3x-2x-6=0

x(x+3)-2(x+3)=0

(x+3) (x-2)=0