Question

The number of positive integral solutions of

$\frac{x^{2}(3x - 4)^{3}(x - 2)^{4}}{(x - 5)^{5}(2x - 7)^{6}}$£ 0 is

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (B)

3

Answer 2

$\frac{x^{2}(3x - 4)^{3}(x - 2)^{4}}{(x - 5)^{5}(2x - 7)^{6}}$ £ 0

Ž x = 0, $\frac{4}{3}$, 2, 3x – 4 < 0, x – 5 > 0

or 3x – 4 > 0 x – 5 < 0

[Q x², (x – 2)⁴, (2x – 7)⁶ > 0]

Ž x = 0, $\frac{4}{3}$, 2, x < $\frac{4}{3}$ , x > 5 or x > 4/3, x < 5

Ž x = 0, 2 and intergral value between

4/3 < x < 5 i.e. x = 2, 3, 4.

Hence positive integral solutions are 2, 3, 4.