Question

if x+1/x=2 then find value of x³+1/x³​

Answer 1

GIVEn

if x+1/x=2 then find value of x³+1/x³

SOLUTIOn

**Cube both side**

→ (x + 1/x)³ = (2)³

Apply identity :

(a + b)³ = a³ + b³ + 3ab(a + b)

→ x³ + 1/x³ + 3*x*1/x(x + 1/x) = 8

→ x³ + 1/x³ + 3 × 2 = 8

→ x³ + 1/x³ + 6 = 8

→ x³ + 1/x³ = 8 - 6

→ x³ + 1/x³ = 2

SOMe IDENTITIEs

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)

Answer 2

IF,

x+1/x=2

then,

x+1=2 x

2 x-x=1

x=1

now, x^3+1/x^3=(1)^3+1/(1)^3

1+1/1=1+1

=2

HOPE IT HELPS