Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If a + b = x, aw + bw 2 = y and aw 2 + bw = z then prove that x 2 + y 2 + z 2 = 6ab
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. L.H.S. x 2 + y 2 + z 2
= (a + b) 2 + (a ω + b ω 2 ) 2 + (a ω 2 + b ω ) 2 = a
2 + b 2 + 2ab + a 2 ω 2 + b 2 ω 4 + 2ab ω 3 +
a 2 ω 4 + b 2 ω 2 + 2ab ω 3 = a
2 + b 2 + 2ab + a 2 ( ω 2 + ω 4 ) + b 2 ( ω 4 + ω 2 ) + 2ab + 2ab ( ω 3 = 1), ( ω 4 = ω 3 . ω = ω )
= a 2 + b 2 + 6ab + a 2 ( ω 2 + ω ) + b 2 ( ω + ω 2 )
= a 2 + b 2 + 6ab + a 2 (–1) + b 2 (–1)
= a 2 + b 2 + 6ab – a 2 – b 2 = 6ab = R.H.S
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems