Question

$A = \frac{0.125 + 0.729}{0.25 - 0.45 + 0.81} - 0.25 + \frac{12}{20} - \frac{6}{8}$
ആയാൽ, A-യുടെ വില എത്രയാണ്?

• A. 1
• B. 1.4
• C. 0
• D. 2

Answer 1

Answer:

A. 1

The value of A is 1.

1. Simplify the first fraction using an algebraic identity:
Notice that the first fraction is in the form of the algebraic cube identity $\frac{a^3 + b^3}{a^2 - ab + b^2} = a + b$:

• $0.125 = (0.5)^3$

• $0.729 = (0.9)^3$

• $0.25 = (0.5)^2$

• $0.45 = 0.5 \times 0.9$

• $0.81 = (0.9)^2$

Applying the identity:
$\frac{(0.5)^3 + (0.9)^3}{(0.5)^2 - (0.5)(0.9) + (0.9)^2} = 0.5 + 0.9 = \mathbf{1.4}$

2. Convert the remaining fractions into decimals:

• $\frac{12}{20} = \frac{3}{5} = \mathbf{0.6}$

• $\frac{6}{8} = \frac{3}{4} = \mathbf{0.75}$

3. Substitute these values back into the expression for A:
$A = 1.4 - 0.25 + 0.6 - 0.75$

4. Perform final addition and subtraction:

• Group the positive numbers: $1.4 + 0.6 = 2.0$

• Group the negative numbers: $-(0.25 + 0.75) = -1.0$

$A = 2.0 - 1.0 = \mathbf{1}$