Question

If 9 − x²> |x − a| has atleast one negative solution, where

a ∈ R then complete set of values of a is

• A. (−25/2, 0)
• B. (−35/4, 0)
• C. (−37/2, 0)
• D. (−37/4, 0)

Answer 1

Answer: (D)

(−37/4, 0)

Answer 2

|x – a| < 9 – x²

⇒ x² – 9 < x – a < 9 – x² = 5 > x² – x – 9 < −a < 9 – x² – x

⇒ 9 + x – x² > a > x² + x – 9 = $\left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 }$

for x ∈ R⁻, 9 + x − x² < 9 and $\left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } \geq - \frac { 37 } { 4 }$

⇒ 0 > a > $- \frac { 37 } { 4 }$