Question

What should be added from the following in the expression 3x^(2)+2x+(1)/(12x^(2)) to make it a perfect square (x!=0)​

Answer 1

Answer:

1- 2x   & -(2x + 1)

Step-by-step explanation:

3x² + 2x +1/12x²

3(x² + (2/3)x +1/36x²)

3(x² + (2/3)x + (1/6x)²)

If it is a perfect square of

√3(x + 1/6x) then

3(x² + 1/36x² + (2/6))

= 3x² + 1/12x²  +  1

to find what to be added

3x² + 1/12x²  +  1 - 3x² + 2x +1/12x²

= 1- 2x

If it is a perfect square of

√3(x - 1/6x) then

3(x² + 1/36x² - (2/6))

= 3x² + 1/12x²  -  1

to find what to be added

3x² + 1/12x²  -  1 - 3x² + 2x +1/12x²

= -1- 2x

= -(2x + 1)