Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
Advertisements
Solution
We have been given
`1/x-1/(x-2)=3`
-2 = 3x2 - 6x
3x2 - 6x + 2 = 0
`3x^2 - (3 + sqrt3)x-(3-sqrt3)x+3-sqrt3+sqrt3-1=0`
`x(3x-3-sqrt3)+((-3+sqrt3)/3)(3x-3-sqrt3)=0`
`((3x-3+sqrt3)/3)(3x-3-sqrt3)=0`
`(sqrt3x-sqrt3+1)(sqrt3x-sqrt3-1)=0`
Therefore,
`sqrt3x-sqrt3+1=0`
`sqrt3x=sqrt3-1`
`x(sqrt3-1)/sqrt3`
or
`sqrt3x-sqrt3-1=0`
`sqrt3x=sqrt3+1`
`x(sqrt3+1)/sqrt3`
Hence, `x(sqrt3-1)/sqrt3` or `x(sqrt3+1)/sqrt3`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6`
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
Find the consecutive numbers whose squares have the sum 85.
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Solve each of the following equations by factorization:
`x+1/x=2.5`
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
Solve the Following Equation : x2- x - a (a + 1) = o
If `sqrt (2/3)` is a solution of equation 3x2 + mx + 2 = 0, find the value of m.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
Solve the following equation by factorization
x (2x + 1) = 6
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
The product of two successive integral multiples of 5 is 300. Then the numbers are:
At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
