Question

(X-(2+root3)(X-(2-root3) solve it

Answer 1

[x-(2+√3)][x-(2-√3)]
= (x-2-√3)(x-2+√3)
= (x-2)^3 - (√3)^2
=x^2 +4 -4x - 3
= x^2 -4x +1

Answer 2

The given expression:

(x - (2 + $\sqrt{3}$))(x - (2 - $\sqrt{3}$))

We have to simply the given expression.

Solution:

∴ (x - (2 + $\sqrt{3}$))(x - (2 - $\sqrt{3}$))

= (x - 2 - $\sqrt{3}$)(x - 2 + $\sqrt{3}$)

= [(x - 2) - $\sqrt{3}$][(x - 2) + $\sqrt{3}$]

Using the algebraic identity:

(a + b)(a - b) = $a^{2} -b^{2}$

= [$(x - 2)^2$ - $(\sqrt{3})^2$]

Using the algebraic identity:

$(a-b)^2$ = $a^{2} +b^{2}-2ab$

= $x^2+2^2-2(x)(2)$ - 3

= $x^2$ + 4 - 4x - 3

= $x^2$ - 4x + 1

∴ (x - (2 + $\sqrt{3}$))(x - (2 - $\sqrt{3}$)) = $x^2$ - 4x + 1