নিচের কোন সমীকরণটির একটি মূল 2 + i√3
Solution
Correct Answer: Option C
অপশন (A)-
x2 + 4x - 7 = 0
= (2 + i√3)2 + 4(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 + 8 + 4√3i - 7
= 4 + 8√3i - 3 + 1
= 8√3i + 2 ≠ 0
অপশন (B)-
x2 - 3x - 7
= (2 + i√3)2 - 3(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 - 6 - 3√3i - 7
= 4 + √3i - 3 - 13
= √3i - 12 ≠ 0
অপশন (C)-
x2 - 4x + 7
= (2 + i√3)2 - 4(2 + i√3) + 7
= 4 + 4√3i + (i√3)2 - 8 - 4√3i + 7
= 4 - 3 - 8 + 7
= 11 - 11
= 0
অপশন (D)-
x2 - 4x - 7 = 0
= (2 + i√3)2 - 4(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 - 8 - 4√3i - 7
= 4 - 3 - 8 - 7
= - 14 ≠ 0
অতএব অপশন (C) সঠিক উত্তর।
x2 + 4x - 7 = 0
= (2 + i√3)2 + 4(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 + 8 + 4√3i - 7
= 4 + 8√3i - 3 + 1
= 8√3i + 2 ≠ 0
অপশন (B)-
x2 - 3x - 7
= (2 + i√3)2 - 3(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 - 6 - 3√3i - 7
= 4 + √3i - 3 - 13
= √3i - 12 ≠ 0
অপশন (C)-
x2 - 4x + 7
= (2 + i√3)2 - 4(2 + i√3) + 7
= 4 + 4√3i + (i√3)2 - 8 - 4√3i + 7
= 4 - 3 - 8 + 7
= 11 - 11
= 0
অপশন (D)-
x2 - 4x - 7 = 0
= (2 + i√3)2 - 4(2 + i√3) - 7
= 4 + 4√3i + (i√3)2 - 8 - 4√3i - 7
= 4 - 3 - 8 - 7
= - 14 ≠ 0
অতএব অপশন (C) সঠিক উত্তর।
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