Question

X + 1/x = 16 Find x-1/x

Answer 1

Answer:

√(212)

Step-by-step explanation:

given x+(1/x)=16

squaring on both sides

[ x+(1/x) ]^2=16^2

x^2+(1/x)^2+2(x)(1/x)=216

x^2+(1/x)^2+2=216

x^2+(1/x)^2=214

then

[x-(1/x)]^2=x^2+(1/x)^2-2(x)(1/x)

[x-(1/x)]^2=x^2+(1/x)^2-2

[x-(1/x)]^2=214-2

[x-(1/x)]^2=212

taking square on other side then it becomes square root

x-(1/x)=√(212)

Answer 2

Step-by-step explanation:

$\frac{x + 1}{x} = 16 \: find \frac{x - 1}{x} \\ = > \frac{x + 1}{x} = 16 \\ = > x + 1 = 16x \\ = > 16x - x = 1 \\ = > 15x = 1 \\ = > x = \frac{1}{15} \\ now \: substituing \: the \: value \: of \: x \\ = \frac{x - 1}{x} \\ = \frac{ \frac{1}{15 } - 1 }{ \frac{1}{15} } = \frac{ \frac{1 - 15}{15} }{ \frac{1}{15} } = \frac{ - 14}{15} \times \frac{15}{1} \\ = - 14$

hence required value of given equation is -14

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