Question

factorise using identity 3x² + 6 + 3/x^2​

Answer 1

$\rm :\longmapsto 3x^2 + 6 + \dfrac{3}{x^2}$

$\rm :\longmapsto 3\left(x^2 + 2 + \dfrac{1}{x^2}\right)$

$\rm :\longmapsto 3 \left[(x)^2 + 2\times x \times \dfrac{1}{x} + \left(\dfrac{1}{x}\right)^2\right]$

$\boxed{\boxed{\rm :\longmapsto 3\left(x+\dfrac{1}{x}\right)^2}}$

Identities used:

$\boxed{\rm :\longmapsto (a+b)^2 = a^2+b^2+2ab}$

Answer 2

Step-by-step explanation:

★Given

★Factorise using identity

• ✪Equation☟︎︎︎
• $\tt\large\underline{3x² + 6 + \frac{3}{x^{2} } }$

★To Find

Factorise Using Identifies.

★Solution

$\tt\large\underline{\longmapsto3x² + 6 + \frac{3}{x^{2} } }$

Multiplying the whole equation by x²

★

3x^2(x^2+1)+3(x^2+1)}

$\large{✰} \bf \underline\color{pu}{\longmapsto(3x^2+3)(x^2+1)}$

$\begin{gathered}\:\:\:\:\:\:\:\:\tt\color{aqua}{●\mid} \underbrace{\color{red}{\longmapsto3x^4+3x^2+3x^2+3}}\color{blue}{\mid●}\\\end{gathered}●∣$

★Therefore,

$\tt\large\underline\orange{\longmapsto'3x^4+6x^2+3'}$

★Identities Used For It-

$\tt\large\underline{\longmapsto(a+b)^2 = a^2+b^2+2ab}$

$\tt\large\underline{\longmapsto(a+b)2=a2+b2+2ab}$

★Some Identifies

• Identity I: (a + b)2 = a2 + 2ab + b2

• Identity II: a2 – b2= (a + b)(a – b)