Question

solve 5x+1/x-6=0,x is not equal to 0 by factorisation

Answer 1

Question :

Solve 5x + 1/x -6 =0, x is not equal to zero. Find the value of x by factorization method.

Solution :

we have given condition,

$\tt5x + \frac{1}{x} - 6 = 0. \: \: x \: \cancel{ = } \: 0.$

Now,

$\implies \tt5x + \frac{1}{x} - 6 = 0. \\ \implies\tt \frac{5 {x}^{2} + 1 - 6x }{x} = 0.$

$\implies \tt5 {x }^{2} - 6x + 1 = 0.$

$\implies \tt5 {x}^{2} - 5x - x + 1 = 0.$

$\implies \tt 5x(x - 1) - 1(x - 1)= 0.$

$\implies \tt(5x - 1)(x - 1) = 0.$

$\implies \tt(5x - 1)= 0. \\ \implies \tt x = \frac{1}{5}$

And,

$\implies \tt(x - 1) = 0. \\ \implies \tt x = 1.$

Therefore,the value of x= 1 and x= 1/5.