Question

If x = 1 + √ , find the value of ( x - ) ^3

Answer 1

Step-by-step explanation:

There are 3 values for x:

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.

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