Question

factorise: 1/144+x/3+4x²​

Answer 1

Answer:

1/144+x/3+4x^2

=(1/12)^2+2.1/12.2x+(2x)^2

=(1/12+2x)^2

Answer 2

1/144 + x/3 + 4x^2

To make the equation easier to factorise, we take LCM (or multiply it by 144 only when there is 0 on the other side of the equation)

= (144*4x^2 + 48x + 1)/114

We find the suitable factors: +24 and +24

= (144*4x^2 + 24x + 24x + 1)/144

= (24(24x + 1) + 1(24x+1))/144

Pls see that this can also be written in the form $a^{2} + b^{2} + 2ab = (a+b)^2$, but I am still making the factors as someone might not see this at first time

= (24x + 1)(24x + 1)/144

To find the answers, we equate the equation to 0

(24x + 1)^2/144 = 0

(24x + 1) = 0

24x = -1

x = -1/24 : Ans

We have 2 same answers here

Hope I helped ☺☻