x 3 n y 3 n is divisible by x y if 451020859

$${x^{{3^n}}} + {y^{{3^n}}}$$ is divisible by $$x + y$$ if

A. $$n$$ is an integer $$ \geqslant 0$$

B. $$n$$ is an odd positive integer

C. $$n$$ is an even positive integer

D. $$n$$ is a rational number

Answer : $$n$$ is an integer $$ \geqslant 0$$

Solution :
$${x^{{3^n}}} + {\left( { - x} \right)^{{3^n}}} = 0\,\,{\text{if }}n \geqslant 0$$ and $$n$$ is an integer.

Releted MCQ Question on
Algebra >> Quadratic Equation

Releted Question 1

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

A. Real and equal

B. Complex

C. Real and unequal

D. None of these

View Answer

Releted Question 2

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

A. Only one solution

B. Only two solutions

C. Infinite number of solutions

D. None of these

View Answer

Releted Question 3

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

A. are real and negative

B. have negative real parts

C. both (A) and (B)

D. none of these

View Answer

Releted Question 4

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

A. positive

B. real

C. negative

D. none of these.

View Answer

$${x^{{3^n}}} + {y^{{3^n}}}$$ is divisible by $$x + y$$ if

Releted MCQ Question on
Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

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Quadratic Equation

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$${x^{{3^n}}} + {y^{{3^n}}}$$ is divisible by $$x + y$$ if

Releted MCQ Question on Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

Practice More Releted MCQ Question on Quadratic Equation

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Releted MCQ Question on
Algebra >> Quadratic Equation

Practice More Releted MCQ Question on
Quadratic Equation