Question

x+1/x=1 , then find the value of x^3 + 1​

Answer 1

Step-by-step explanation:

1

If x+1/x=3,then what will be the value of x?

Case 1:

x+1x=3

x+1=3x

2x=1

x=12

Case 2:

x+1x=3

x2+1x=3

x2−3x+1=0

x=−(−3)±(−3)2−4(1)(1)√2⋅1

x=3±5√2

If you take it as (x+1)/x = 3, then

x+1 = 3x, or

2x = 1, or

x = 0.5

Check: (0.5+1)/0.5 = 3. Correct

If you take it as x + (1/x) = 3, then

x^2–3x+1 = 0

x1 = [3+(9-4)^0.5]/2 = [3+5^0.5]/2 = 2.618033989.

x2 = [3-(9-4)^0.5]/2 = [3–5^0.5]/2 = 0.381966011.

Check: x1+(1/x1) = 2.618033989+(1/2.618033989) = 3. Correct.

x2+(1/x2) = 0.381966011+(1/0.381966011) = 3. Correct.

x1 = 2.618033989.

x2 = 0.381966011.

Answer 2

Answer:

x+1/x=1

(x+1/x)³=x³+1/x³+3x. 1/x(x+1/x)

1³=x³+1/x³+3(1)

1-3=x³+1/x³

x³+1/x³=-2

HOPE THIS HELPS