Question

The number of negative solution (s) of the equation | x | – 2 | x + 1 | + 3 | x + 2 | = 0 is (are) –

• A. 1
• B. 2
• C. 4
• D. Infinite

Answer 1

Answer: (C)

4

Answer 2

$(1.25)^{1 - x^{2}}$– (0.4096)^1+x > 0

̃ $\left( \frac{5}{4} \right)^{1 - x^{2}}$– $\left( \frac{5}{4} \right)^{- 4 - 4x}$> 0

̃ $\left( \frac{5}{4} \right)^{1 - x^{2}}$> $\left( \frac{5}{4} \right)^{- 4(1 + x)}$

̃ 1 – x² > – 4 (1 + x)

̃ x² – 4x – 5 < 0 ̃ x Î (–1, 5)

\ a = –1, b = 5 ̃ a + b = 4