Question

If x + y + z = 5 and xy + yz +zx = 3, then least and largest value of x are:

• A. $\frac{10}{3}$, 5
• B. – 1, $\frac{13}{3}$
• C. $\frac{17}{3}$, 7
• D. None of these

Answer 1

Answer: (B)

– 1, $\frac{13}{3}$

Answer 2

xy + y (5 –x –y) + x (5 –x – y) = 3

or xy + 5y –xy –y² + 5x –x² –xy = 3

or 5y – y² + 5x –x² – xy = 3

or y² + (x – 5) y + (x² –5x + 3) = 0

since y Ī R, D ³ 0

Ž (x – 5)² – 4 (x² –5x + 3) ³ 0

or –3x² + 10x + 13 ³ 0

or 3x² – 10x –13 £ 0

or 3x² + 3x –13x – 13 £ 0

or (3x – 13) (x + 1) £ 0