If x+(1)/(x)=-3 then the value of x^(8)+3x^(7)+x^(6)+5 is
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Answer:
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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