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Paragraph: Let and be the roots of the equation x ^2- (1-2 a ^2 ) x + (1-2 a ^2 )=0 Question: Under what condition is 1 ^2 + 1 ^2 1 ?

Options

  1. Aa ^2 1 2
  2. Ba^2 1 2
  3. Ca^2 1
  4. Da ^2 ( 1 3 , 1 2 ) only

Correct answer

A. a ^2 1 2

Step-by-step solution

1 ^2 + 1 ^2 1 ^2+ ^2 ( )^2 1 aligned & ( + )^2-2 ( )^2 1 & + = -b a = (1-2 a ^2 ) & = c a = (1-2 a ^2 ) & On solving: 1 aligned aligned & 4 a^4-1 4 a^4-4 a^2+1 & 4 a^4-1 4 a^4-4 a^2+1 & 4 a^2 2 a^2 1 2 aligned

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