Discussion

Question:

A, B and C are defined as follows.

A = 2.000004 ÷ [(2.000004)² + (4.000008)]

B = 3.000003 ÷ [(3.000003)² + (9.000009)]

C = 4.000002 ÷ [(4.000002)² + (8.000004)]

Which of the following is true about the values of the above three expressions?

Explanation:

$A = \frac{2.000004}{[{(2.000004)}^{2} + 2 (2.000004)]}$

$= \frac{2.000004}{2.000004 [(2.000004) 2]}$

= $\frac{1}{[(2.000004) 2]}$

$= \frac{1}{4.000004}$

= $\frac{1}{4} = 0.25$ (Approximately)

$B = \frac{3.000003}{[{(3.000003)}^{3} + 3 (3.000003)]}$

$= \frac{3.000003}{3.000003 [(3.000003) 3]}$

$= \frac{1}{[(3.000003) 3]} = \frac{1}{6.000003}$

$C = \frac{4.000002}{[{(4.000002)}^{2} + 2 (4.000002)]}$

$= \frac{4.000002}{4.000002 [(4.000002) 2]}$

$= \frac{1}{[(4.000002) 2]} = \frac{1}{6.000002}$

Looking at the answer choices, we can see that the only (d) satisfies the relationship, viz. B is the smallest.

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