Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If x + y + z = 5 and xy + yz + zx = 3, then least and largest value of x are:
Text Solution
Verified by ExpertsThe correct answer is:
B
xy + y (5 –x –y) + x (5 –x – y) = 3
or xy + 5y –xy –y 2 + 5x –x 2 –xy = 3
or 5y – y 2 + 5x –x 2 – xy = 3
or y 2 + (x – 5) y + (x 2 –5x + 3) = 0
since y ∈ R, D ≥ 0
⇒ (x – 5) 2 – 4 (x 2 –5x + 3) ≥ 0
or –3x 2 + 10x + 13 ≥ 0
or 3x 2 – 10x –13 ≤ 0
or 3x 2 + 3x –13x – 13 ≤ 0
or (3x – 13) (x + 1) ≤ 0
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