Question

Find a^3-1/a^3 if a-1/a=14

Answer 1

Answer:

2786

Step-by-step explanation:

a-1/a=14

Cubing on both sides

a^3-1/a^3-3(a-1/a)=14^3

a^3-1/a^3=2744+3(14)=2786

Answer 2

ANSWER:

a³ - 1/a³ = 2786

GIVEN:

a - (1 / a) = 14

TO FIND:

a³ - (1/a³) = ??

FORMULA:

(A - B)² = A² - 2AB + B²

(A - B)²(A-B) = (A - B)³

(A - B)³ = (A² - 2AB + B²)(A-B)

(A - B)³ = A³ - 2A²B - B³ + 2AB²

EXPLANATION:

Apply square on both sides.

(a - 1/a)² = 14²

a² - 2a × 1/a + 1/a² = 196

a² - 2 +b1/a² = 196

a² + 1/a² = 198

Multiply by a - (1 / a) on left side and by 14 on right sides as a - (1 / a) = 14

(a² + 1/a²)(a - 1/a) = 198 × 14

a³ - a + 1/a - 1/a³ = 2772

a³ - 1/a³ - (a - 1/a) = 2772

a³ - 1/a³ - 14 = 2772

a³ - 1/a³ = 2786