If x 2 6x 1 0 then the value of left x 6 right 3 frac 1 left x 6 right 3 ........

Quantitative Aptitude (CPO) Algebra

If $$x^{2} + 6x+ 1 = 0$$, then the value of $$\left(x + 6\right)^{3} + \frac{1}{\left(x + 6\right)^{3}}$$ = ?

This questions was previously asked in

SSC CPO 10th Nov 2022 Shift 3

245

216

186

198

- Given: The quadratic equation is $x^2 + 6x + 1 = 0$.

- Objective: Find the value of $(x + 6)^3 + \frac{1}{(x + 6)^3}$.

- Transform: Let $y = x + 6$, then $x = y - 6$.

- Substitute in Equation: $(y - 6)^2 + 6(y - 6) + 1 = 0$.

- Simplify: This becomes $y^2 - 12y + 37 = 0$.

- Expression to Find: $(x+6)^3 + \frac{1}{(x+6)^3} = y^3 + \frac{1}{y^3}$.

- Use Identity: If $y + \frac{1}{y} = 12$, then $y^3 + \frac{1}{y^3} = 12^3 - 3(12)$.

- Calculate: $12^3 - 36 = 198$.

- Answer: Option 4: 198

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