If a+b = 3 and a-b = 1, find the value of a4 - b4.
Show answer & explanation
Correct answer: A
Explanation
Given:
a + b = 3
a − b = 1
By the formula:
a² − b² = (a + b)(a − b)
a⁴ − b⁴ = (a² − b²)(a² + b²)
a² − b² = (3)(1) = 3
(a + b)² = a² + 2ab + b²
9 = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
1 = a² − 2ab + b²
Add the two:
10 = 2(a² + b²)
a² + b² = 5
a⁴ − b⁴ = (a² − b²)(a² + b²)= 3 × 5= 15