AI-তৈরি নমুনা উত্তর
প্রদত্ত রাশি:1 − i x 2 − 1 1 - i\sqrt{x^2 - 1} 1 − i x 2 − 1 = 1 2 [ 2 − 2 i x 2 − 1 ] = \frac{1}{2} \left[ 2 - 2i\sqrt{x^2 - 1} \right] = 2 1 [ 2 − 2 i x 2 − 1 ] = 1 2 [ ( x + 1 ) − 2 x + 1 ⋅ i x − 1 − ( x − 1 ) ] = \frac{1}{2} \left[ (x + 1) - 2\sqrt{x+1} \cdot i\sqrt{x-1} - (x - 1) \right] = 2 1 [ ( x + 1 ) − 2 x + 1 ⋅ i x − 1 − ( x − 1 ) ] = 1 2 [ ( x + 1 ) 2 − 2 ⋅ x + 1 ⋅ ( i x − 1 ) + ( i x − 1 ) 2 ] = \frac{1}{2} \left[ (\sqrt{x+1})^2 - 2 \cdot \sqrt{x+1} \cdot (i\sqrt{x-1}) + (i\sqrt{x-1})^2 \right] = 2 1 [ ( x + 1 ) 2 − 2 ⋅ x + 1 ⋅ ( i x − 1 ) + ( i x − 1 ) 2 ] = 1 2 ( x + 1 − i x − 1 ) 2 = \frac{1}{2} \left( \sqrt{x+1} - i\sqrt{x-1} \right)^2 = 2 1 ( x + 1 − i x − 1 ) 2
অতএব, প্রদত্ত রাশির বর্গমূল:= ± 1 2 ( x + 1 − i x − 1 ) = \pm \frac{1}{\sqrt{2}} \left( \sqrt{x+1} - i\sqrt{x-1} \right) = ± 2 1 ( x + 1 − i x − 1 )