Home
Class 12
MATHS
If omega ne 1 is a cube root of unity an...

If `omega ne 1` is a cube root of unity and `a+b=21`, `a^(3)+b^(3)=105`, then the value of `(aomega^(2)+bomega)(aomega+bomega^(2))` is be equal to

A

`3`

B

`5`

C

`7`

D

`35`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(aomega^(2)+bomega)(aomega+bomega^(2))=a^(2)-ab+b^(2)`
`= ((a+b)(a^(2)-ab+b^(2)))/(a+b)`
`=(a^(3)+b^(3))/(a+b)=(105)/(21)=5`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

If omega(ne1) is a cube root of unity and (1+omega)^7=A+B_omega then (A,B) equals

If omega is an imaginary cube root of unity, then the value of (1+ omega- omega^(2))(1- omega + omega ^(2)) is-

If 1, omega, omega^(2) are the cube roots of unity, then the value of |(1,omega^(n),omega^(2n)),(omega^(n),omega^(2n),1),(omega^(2n),1,omega^(n))| is equal to -

If omega is a cube root of unity then the value of |(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)| is -

If omega ne 1 is a cube root of unity , then find the value of |{:(1+2omega^(100)+omega^(200)," "omega^2," "1),(" "1,1+omega^(100)+2omega^(200)," "omega),(" "omega," "omega^2,2+omega^(100)+omega^(200)):}|=0

If omega is a complex cube root of unity, then the value of (2-omega) (2-omega ^(2)) (2- omega ^(10)) (2- omega ^(11)) will be-

If 1, omega, omega ^(2) are the cube roots of unity, then the value of (x+y) ^(2) + (x omega +y omega ^(2))^(2) + (x omega ^(2)+ y omega )^(2) is equal to-

If omega(ne1) be a cube root of unity and (1+omega^2)^n=(1+omega^4)^n then the least positive value of n is

If omega is a complex cube root of unity then the value of [225 + ( 3 omega + 8 omega ^(2))^(2) +(3 omega ^(2) + 8 omega )^(2)] is-

If omega is an imaginary cube root of unity then the value of (2-omega),(2-omega^(2))+2(2-omega)(3-omega^(2))+....+(n-1)(n-omega)(n-omega^(2)) is