Question
Download Solution PDFSimplify the given expression. \(\frac{[1.5 \times 1.5 \times 1.5+2.7 \times 2.7 \times 2.7+4.8 \times 4.8 \times 4.8-3 \times 1.5 \times 2.7 \times 4.8]}{[1.5 \times 1.5+2.7 \times 2.7+4.8 \times 4.8-1.5 \times 2.7-2.7 \times 4.8-4.8 \times 1.5]}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simplify the expression:
\(\frac{[1.5 \times 1.5 \times 1.5+2.7 \times 2.7 \times 2.7+4.8 \times 4.8 \times 4.8-3 \times 1.5 \times 2.7 \times 4.8]}{[1.5 \times 1.5+2.7 \times 2.7+4.8 \times 4.8-1.5 \times 2.7-2.7 \times 4.8-4.8 \times 1.5]}\)
Formula used:
The expression follows the identity for a determinant involving three variables:
(a3 + b3 + c3 - 3abc) / (a2 + b2 + c2 - ab - bc - ca) = a + b + c
Calculation:
Let a = 1.5, b = 2.7, and c = 4.8.
Using the formula:
Numerator = 1.53 + 2.73 + 4.83 - 3(1.5)(2.7)(4.8)
Denominator = 1.52 + 2.72 + 4.82 - (1.5 × 2.7) - (2.7 × 4.8) - (4.8 × 1.5)
Applying the identity, we get:
a + b + c = 1.5 + 2.7 + 4.8 = 9
∴ The simplified value of the expression is 9.
Last updated on Jun 3, 2025
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