Question

Factorize:- b) 3x^2+6+ 3/ x^2​

Answer 1

Answer:

3x^2+6+3/x^2

=3[x^2+1/x^2]=-6

let take x^2+1/x^2=y

then 3y=-6

y=-2

then

x^2+1/x^2=-2

x^2+1/x^2+2=0

in this we use (a+b) ^2=a^2+2ab+b^2

(x+1/x)^2=0

Answer 2

Answer:

After factorization, the equation becomes $3x^{2}+6+\frac{3}{x^{2}}=3(x+\frac{1}{x} )^{2}$.

Step-by-step explanation:

Given equation is $3x^{2}+6+\frac{3}{x^{2}}$.

We have to factorize the given equation.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

From the given equation, take out the number $3$ as common,

$3(x^{2}+2+\frac{1}{x^{2}})$.

Now the remaining term is $x^{2}+2+\frac{1}{x^{2}}$

We can write $1=x\times \frac{1}{x}$ (since both cancels out)

Now substitute the above value in the equation.

$x^{2} +2(x\times\frac{1}{x})+\frac{1}{x^{2} }$

$=(x)^{2}+2(x\times\frac{1}{x})+(\frac{1}{x})^{2}$

We know the formula $(a+b)^{2}=a^{2}+2ab+b^{2}$.

By using the formula, the above equation simplifies to $(x+\frac{1}{x} )^{2}$.

The given equation becomes

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

Hence the equation is factored.