Find x for the equation: x+1/x = -1 (x plus one divided by x equals negative one)
+33654 A. If you mean x + (1/x) = -1 then:
Multiply all terms by x:
x2 + 1 = -x
Add x to both sides:
x2 + x + 1 = 0
Solve:
x2+x+1=0⇒{x=−(√3×i+1)2x=(√3×i−1)2}⇒{x=−(12+0.866025403785i)x=−12+0.866025403785i}
B. If you mean (x + 1)/x = -1
Multiply both sides by x
x + 1 = -x
Add x to both sides
2x + 1 = 0
Subtract 1 from both sides
2x = -1
Divide both sides by 2
x = -1/2
.
+26396 Find x for the equation: x+1/x = -1 (x plus one divided by x equals negative one)
set 1x=−1−x and see there is no cut between function 1x and line −1−x
+118703 For
x+(1/x) = -1
Alan and Heureka are both telling you that there are no real solutions.
Alan has said x cannot equal 0 because you cannot divide by 0
Alan has rearranaged the equation to give a quadratic.
x2+x+1=0
For any quadratic you can determine the nature of the roots by examining the discriminate
△=b2−4ac△=1−4=−3
Since the discriminant (which is under a square root) is negative, there are no real roots.
+130466 Thanks for that reminder about the discriminant, Melody......this should always be kept in mind when searching for "real" roots in a quadratic (it can save us some unnecessary work !!!)
