How do you solve $x+ \frac { 6 } { x } = 5$ ?

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Answer 1 · 2016-10-12T02:58:27

$x=2$ and $x=3$

I would approach this problem by finding the common denominator on both sides of the equation then simplify the equation.

$x+6/x=5$

The common denominator (LCD) is $x$

$(x^2+6)/(1 cancel x)=(5x)/(1 cancel x)$

Simplify the $x$ 's or use another method but you will see that you will end up simplifying the $x$

$x^2+6=5x$

$x^2-5x+6=0$

Here, too you can use any method you are comfortable with, as for me I always find the $Delta$

$Delta=b^2-4ac$ , with $a=1$ , $b=-5$ and $c=6$

$Delta=(-5)^2-4(1)(6)=1=>sqrt Delta=+-1$

$x_1=(-b+sqrt Delta)/(2a)$ and $x_2=(-b-sqrt Delta)/(2a)$

$x_1=(5+1)/(2)=3$ and $x_2=(5-1)/(2)=2$

So, $x=2$ and $x=3$ is your solution.

How do you solve x+ \frac { 6 } { x } = 5x+ \frac { 6 } { x } = 5?