Which option is correct?

If xyz=1xyz=-1, then the value of (xyz)44 \sqrt [ 4 ]{ \left( xyz \right)^4 } is

Option 1 : 1

Why?

Because

(xyz)44=(1)44=14=1\Large{ \sqrt [ 4 ]{ \left( xyz \right)^4} =\sqrt [ 4 ]{ \left( -1 \right) ^{ 4 } } =\sqrt [ 4 ]{ 1 } =1}

Option 2 : -1

Why?

Because

(xyz)44=xyz=1\Large{\sqrt [ 4 ]{ \left( xyz \right) ^{ 4 } }=xyz=-1}

Option 3 : ii

Why?

Because

(xyz)44=(xyz)34×xyz4=i×i=i\Large{\sqrt [ 4 ]{ \left( xyz \right) ^{ 4 } } =\quad \sqrt [ 4 ]{ \left( xyz \right) ^{ 3 } } \times \sqrt [ 4 ]{ xyz } =\sqrt { i } \times \sqrt { i } =i}

Explanation required

Note by Department 8
3 years, 10 months ago

No vote yet
1 vote

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Comments

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I think this one example may help you.
Ex. (1)2(1)2(\sqrt{-1})^2 \neq \sqrt{(-1)^2}
LHS : (1)2=1(\sqrt{-1})^2 = -1
RHS : (1)2=1=1\sqrt{(-1)^2} = |-1| = 1

I think all the options are correct. Given equation has 4 roots.i.e 1,1,ι,ι1 , -1 , \iota , -\iota

Akhil Bansal - 3 years, 10 months ago

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Option 0!0!

Hjalmar Orellana Soto - 3 years, 10 months ago

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Option 1, because the property that (a)^(mn)=a^m*a^n is only preserved for real numbers.

Aditya Agarwal - 3 years, 10 months ago

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Option 1. First condition: xyz= -1

ma pm - 3 years, 10 months ago

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let x = xyz^4 so x will have roots ie i,-1,1,one more

genius literally - 3 years, 10 months ago

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Option 1

Deepak Kumar - 3 years, 10 months ago

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Explanation required

Department 8 - 3 years, 10 months ago

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(x^2n)^(1/2n)=|x|

Deepak Kumar - 3 years, 10 months ago

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@Deepak Kumar Nice

Department 8 - 3 years, 10 months ago

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Ya correct explanation.....its option 1

Ravi Dwivedi - 3 years, 10 months ago

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option 1 guaranteed .option 2-no because the root sign stands for only positive values and option 3 -no because u cant do it for unreal numbers

Kaustubh Miglani - 3 years, 10 months ago

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