मान लीजिए `omega_(1)` और `omega_(2)` एक (यूनिटी) के, 1 से इतर, दो अलग-अलग घनमूल हैं, तो `(omega_(1) - omega_(2))^(2)` किसके बराबर है?

Options

A. 3
B. 1
C. `-1`
D. `-3`

Answer

D

Explanation

दिया है,
`(omega_(1) -omega_(2))^(2) = omega_(1)^(2) + omega_(2)^(2) - 2omega_(1)omega_(2)`
माना `omega_(1) = omega_(2)` और `omega_(2) = omega`
`therefore (omega_(1) - omega_(2)) = (omega^(2))^(2) + omega^(2) - 2omega^(2) * omega`
` = omega^(4) + omega^(2) -2omega^(3)`
` = omega^(3) * omega + omega^(2) -2omega^(3)`
` = omega + omega^(2) - 2 = -1-2 " " [because 1 + omega + omega^(2) = 0]`
`rArr (omega_(1)-omega_(2))^(2) = -3`