Simplify: (1.3*1.3*1.3-1)/(1.3*1.3+1.3+1)
2024
Simplify:
(1.3*1.3*1.3-1)/(1.3*1.3+1.3+1)
- A.
0.3
- B.
31/3
- C.
0.003
- D.
1
Attempted by 3664 students.
Show answer & explanation
Correct answer: A
Key idea: Use the factorization x^3 - 1 = (x - 1)(x^2 + x + 1).
Let x = 1.3. Then the expression becomes (x^3 - 1)/(x^2 + x + 1).
Apply the factorization: (x^3 - 1)/(x^2 + x + 1) = (x - 1)(x^2 + x + 1)/(x^2 + x + 1) = x - 1.
Compute x - 1: 1.3 - 1 = 0.3.
Numeric check: numerator = 1.3^3 - 1 = 2.197 - 1 = 1.197; denominator = 1.3^2 + 1.3 + 1 = 1.69 + 1.3 + 1 = 3.99; 1.197/3.99 = 0.3.
Therefore the simplified value is 0.3.