TS EAMCET · Maths · Complex Number

If $\alpha, \beta$ are non-real cube roots of 2 , then $\alpha^6+\beta^6$ equals

Verified Solution

Answer & Solution

Correct Answer

(A) 8

Step-by-step Solution

Detailed explanation

Since, $\alpha$ and $\beta$ are non-real cube roots of 2 .…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If the function $f(x)=\left\{\begin{array}{cc}\frac{\left(e^{k x}-1\right) \sin k x}{4 \tan x}, & x \neq 0 \ P, & x=0\end{array}\right.$ is differentiable at $x=0$, then

TS EAMCET 2024 Easy
$\frac{1}{\sin 250^{\circ}}+\frac{\sqrt{3}}{\cos 290^{\circ}}=$

TS EAMCET 2022 Easy
For any vector $\mathbf{r}$ $\mathbf{i} \times(\mathbf{r} \times \mathbf{i})+\mathbf{j} \times(\mathbf{r} \times \mathbf{j})+\mathbf{k} \times(\mathbf{r} \times \mathbf{k})$ is equal to

TS EAMCET 2011 Easy
$\lim _{x \rightarrow 0} \frac{\left(2^x-1\right)(1+\sin x)^{\frac{2}{\sin x}}}{\log (1+2 x)}=$

TS EAMCET 2022 Medium
If $A=\left[\begin{array}{rr}-8 & 5 \\ 2 & 4\end{array}\right]$ satisfies the equation $x^2+4 x-p=0$, then $p$ is equal to

TS EAMCET 2013 Medium
The greatest angle of the triangle whose sides are $x^2+x+1,2 x+1$ and $x^2-1$ is

TS EAMCET 2018 Easy

Explore more questions on app

From TS EAMCET

The locus of the mid points of the chords of the circle $x^{2} - 2 x + y^{2} = 0$ drawn from a point $(0, 0)$ on it is

TS EAMCET 2021 Easy
The following system of equations $x + y + z = 9$ $2 x + 5 y + 7 z = 52$ $x + 7 y + 11 z = 77$ has

TS EAMCET 2018 Easy
An integrating factor of the equation $\left(1+y+x^2 y\right) d x+\left(x+x^3\right) d y=0$ is

TS EAMCET 2013 Easy
If $\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\overrightarrow{\mathbf{d}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$, then observe the
following The correct match of List-I to List-II $\begin{array}{llll}\text { i } & \text { ii } & \text { iii } & \text { iv }\end{array}$

TS EAMCET 2008 Easy
Let $\mathbf{v}=2 \mathbf{i}+\mathbf{j}-\mathbf{k}$ and $\mathbf{w}=\mathbf{i}+3 \mathbf{k}$. If $\mathbf{u}$ is any unit vector, then the m$\sqrt{59}$ aximum value of the scalar triple product $[\mathbf{u} \mathbf{v} \mathbf{w}]$ is

TS EAMCET 2011 Medium
A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \mathrm{~ms}^{-1}$ when pressure is $50 \mathrm{kPa}$ at a point. If the velocity of flow has to be $2 \mathrm{~ms}^{-1}$ at some other point, the pressure at that point should be

TS EAMCET 2007 Hard

Explore more questions on app

If \(\alpha, \beta\) are non-real cube roots of 2 , then \(\alpha^6+\beta^6\) equals

Answer & Solution

Step-by-step Solution

See the Complete Solution