solve for x 1÷x-1÷x-2=3
Answers
Answer:
The roots of the quadratic equation \frac{1}{x}-\frac{1}{x-2} = 3
x
1
−
x−2
1
=3 are x =\frac{3+1\sqrt{3}}{3}x=
3
3+1
3
,x =\frac{3-1\sqrt{3}}{3}x=
3
3−1
3
.
Step-by-step explanation:
As given the equation in the form
\frac{1}{x}-\frac{1}{x-2} = 3
x
1
−
x−2
1
=3
Simplify the above equation
(x-2)-x = 3x × (x-2)
x-2 - x = 3x² - 6x
3x² - 6x + 2 = 0
As the equation is written in the form ax² + bx + c = 0
x =\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}x=
2a
−b±
b
2
−4ac
a = 3 , b = -6 , c = 2
Put all the values in the above equation
x =\frac{-(-6)\pm\sqrt{(-6)^{2}-4\times 3\times 2}}{2\times 3}x=
2×3
−(−6)±
(−6)
2
−4×3×2
x =\frac{6\pm\sqrt{36-24}}{6}x=
6
6±
36−24
x =\frac{6\pm\sqrt{12}}{6}x=
6
6±
12
x =\frac{6\pm2\sqrt{3}}{6}x=
6
6±2
3
x =\frac{3\pm1\sqrt{3}}{3}x=
3
3±1
3
Thus
x =\frac{3+1\sqrt{3}}{3}x=
3
3+1
3
x =\frac{3-1\sqrt{3}}{3}x=
3
3−1
3
Therefore the roots of the quadratic equation \frac{1}{x}-\frac{1}{x-2} = 3
x
1
−
x−2
1
=3 are x =\frac{3+1\sqrt{3}}{3}x=
3
3+1
3
,x =\frac{3-1\sqrt{3}}{3}x=
3
3−1
3
.