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Find the roots of quadratic equation 1/x - 1/(x - 2) = 3.
Quadratic equations are one of the most integral parts of algebra in mathematics. They find their applications in various fields of engineering and science to find values of different quantities and parameters. These equations can have a maximum of two roots. Now, let's solve a problem related to this concept.
Answer: The roots of the equation 1/x - 1/(x - 2) = 3 are 1 + 1/√3 and 1 - 1/√3.
Let's understand the solution in detail.
The equation given can be re-written as:
⇒ 1/x - 1/(x - 2) = 3
⇒ (x - 2 - x) / x (x - 2) = 3
⇒ - 2 = 3x2 - 6x
⇒ 3x2 - 6x + 2 = 0
This equation is now of the form ax2 + bx + c. Now we can apply the discriminant formula to find the roots.
The roots of the equation come out to be x = 1 + 1/√3 and x = 1 - 1/√3.
Hence, the roots of the equation 1/x - 1/(x - 2) = 3 are 1 + 1/√3 and 1 - 1/√3.