Which of the following is equal to -1-

The correct option is B √(3)+√( 1)/√( 4) x=√( 1) ⇒ x^3= 1 ⇒ ( x)^3=1 ⇒ x=1, ω, ω^2 ⇒ x= 1, ω, ω^2 = 1, 1+√(3)i/2,1 √(3)i ...

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Standard XII

Mathematics

Integration by Partial Fractions

Which of the ...

Question

Which of the following is equal to $\sqrt[3]{- 1}$ ?

\frac{\sqrt{3} + \sqrt{- 1}}{2}

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\frac{- \sqrt{3} + \sqrt{- 1}}{\sqrt{- 4}}

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\frac{\sqrt{3} - \sqrt{- 1}}{\sqrt{- 4}}

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- \sqrt{- 4}

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Solution

The correct option is B $\frac{- \sqrt{3} + \sqrt{- 1}}{\sqrt{- 4}}$
$x = \sqrt[3]{- 1}$
$\Rightarrow x^{3} = - 1$
$\Rightarrow (- x)^{3} = 1$
$\Rightarrow - x = 1, ω, ω^{2}$
$\Rightarrow x = - 1, - ω, - ω^{2}$
$= - 1, \frac{1 + \sqrt{3} i}{2}, \frac{1 - \sqrt{3} i}{2}$
$= - 1, \frac{- \sqrt{3} + i}{2 i}, \frac{\sqrt{3} + i}{2 i}$
$= - 1, \frac{- \sqrt{3} + \sqrt{- 1}}{\sqrt{- 4}}, \frac{\sqrt{3} + \sqrt{- 1}}{\sqrt{- 4}}$

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Which of the following is equal to 3√−1?

The correct option is B −√3+√−1√−4x=3√−1⇒x3=−1⇒(−x)3=1⇒−x=1,ω,ω2⇒x=−1,−ω,−ω2=−1,1+√3i2,1−√3i2=−1,−√3+i2i,√3+i2i=−1,−√3+√−1√−4,√3+√−1√−4

Which of the following is equal to $\sqrt[3]{- 1}$ ?