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Test-1-1-1-1-1-1-i-i-i-2-1-so-1-1-Find-the-error-




Question Number 8600 by Chantria last updated on 17/Oct/16
 Test    1=(√1)=(√((−1)(−1)))=(√(−1))∙(√(−1))                                         =i∙i=i^2 =−1    so 1=−1   Find the error.
Test1=1=(1)(1)=11=ii=i2=1so1=1Findtheerror.
Commented by prakash jain last updated on 17/Oct/16
(ab)^x =a^x ∙b^x    only for a,b,x∈R and a,b,x are +ve.  (−1)^(1/2) (−1)^(1/2) ≠(−1×−1)^(1/2)  since −1<0
(ab)x=axbxonlyfora,b,xRanda,b,xare+ve.(1)1/2(1)1/2(1×1)1/2since1<0
Answered by malwaan last updated on 18/Oct/16
(√1)=±1   so 1=(√1) is one part from the solution  and (√1)=−1 is the 2nd part  1=(√1)=−1 is wrong  (√1)=±1 is right
1=±1so1=1isonepartfromthesolutionand1=1isthe2ndpart1=1=1iswrong1=±1isright
Commented by Rasheed Soomro last updated on 19/Oct/16
“ (√(  )) ” is used only for +ve root.  Hence (√1) = 1 not (√1)=±1  We can write ±(√1)=±1 but  we can′t write (√1)=±1
isusedonlyfor+veroot.Hence1=1not1=±1Wecanwrite±1=±1butwecantwrite1=±1
Commented by FilupSmith last updated on 19/Oct/16
but (√x^2 )=±x  (+x)^2 =x^2   (−x)^2 =(−1)^2 (x)^2 =x^2
butx2=±x(+x)2=x2(x)2=(1)2(x)2=x2
Commented by nume1114 last updated on 19/Oct/16
(√x^2 )=∣x∣  example  if x=3,      (√x^2 )=(√9)=3,∣x∣=3        x=−1,  (√x^2 )=(√1)=1,∣x∣=1        x=0,      (√x^2 )=(√0)=0,∣x∣=0
x2=∣xexampleifx=3,x2=9=3,x∣=3x=1,x2=1=1,x∣=1x=0,x2=0=0,x∣=0

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