Question

താഴെ തന്നിരിക്കുന്നത് ലഘൂകരിക്കുക:

$\frac{6.5^3 - 5^3}{42.25 + 32.5 + 25}$

• A. 3.5
• B. 2.5
• C. 1.5
• D. 0.5

Answer 1

Answer:

C. 1.5

The simplified value of the expression is 1.5 (or $\frac{3}{2}$).

1. Identify the algebraic identity pattern:
The expression is in the form of the algebraic identity:
$\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b$

Let's test this by setting:

• $a = 6.5$

• $b = 5$

2. Verify the terms:

• Numerator: $6.5^3 - 5^3$ matches $a^3 - b^3$

• Denominator values:

  • $a^2 = 6.5^2 = 42.25$

  • $ab = 6.5 \times 5 = 32.5$

  • $b^2 = 5^2 = 25$

Since the denominator is exactly $42.25 + 32.5 + 25$, it matches $a^2 + ab + b^2$ perfectly.

3. Apply the solution:
$a - b = 6.5 - 5 = \mathbf{1.5}$