Question

Find all x ∈ R that solve this equation: 123 = x · (2x · (3x − 3) − 2) + 100 + 20 + 3

Answer 1

Step-by-step explanation:

Find all x ∈ R that solve this equation: 123 = x · (2x · (3x − 3) − 2) + 100 + 20 + 3

Answer 2

Given,

Equation, $\[123 = x \times \left( {2x \times \left( {3x - 3} \right) - 2} \right) + 100 + 20 + 3\]$

Solution,

Know that, $\[x \in R\]$

$\[\begin{array}{l}123 = x \times \left( {2x \times \left( {3x - 3} \right) - 2} \right) + 100 + 20 + 3\\ \Rightarrow 123 = x\left( {6{x^2} - 6x - 2} \right) + 123\\ \Rightarrow x\left( {6{x^2} - 6x - 2} \right) = 0\\ \Rightarrow x\left( {3{x^2} - 3x - 1} \right) = 0\end{array}\]$

Solve the polynomial,

$\[x = 0\]$

$\[3{x^2} - 3x - 1 = 0\]$

Using Shri Dharacharya Formula,

$\[ \Rightarrow x = \frac{{3 \pm \sqrt {{{\left( { - 3} \right)}^2} + 4 \times 3 \times 1} }}{{2 \times 3}}\]$

$\[ \Rightarrow x = \frac{{3 \pm \sqrt {9 + 12} }}{6}\]$

$\[ \Rightarrow x = \frac{{3 \pm \sqrt {21} }}{6}\]$

Hence the value of x are $\[0,\left( {\frac{{3 + \sqrt {21} }}{6}} \right),\left( {\frac{{3 - \sqrt {21} }}{6}} \right)\]$.