Advertisements
Advertisements
Question
Solve the following equation by using formula :
`(1)/(x - 2) + (1)/(x - 3) + (1)/(x - 4)` = 0
Solution
`(1)/(x - 2) + (1)/(x - 3) + (1)/(x - 4)` = 0
⇒ `(1)/(x - 2) + (1)/(x - 3) = -(1)/(x - 4)`
⇒ `(x - 3 + x - 2)/((x - 2)(x - 3)) = -(1)/(x - 4)`
⇒ `(2x - 5)/(x^2 - 5x + 6) = (-1)/(x - 4)`
(2x - 5)(x - 4) = -1(x2 - 5x + 6)
⇒ 2x2 - 8x - 5x + 20 = -x2 + 5x - 6
⇒ 2x2 - 8x - 5x + 20 + x2 - 5x + 6 = 0
⇒ 3x2 - 18x + 26 = 0
Here, a = 3, b = -18, c = 26
∴ x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
= `(-(-18) ± sqrt((-18)^2 - 4 xx 3 xx 26))/(2 xx 3)`
= `(18 ± sqrt(324 - 312))/(6)`
= `(18 ± sqrt(12))/(6)`
= `(18 ± 2sqrt(3))/(6)`
= `(9 ± sqrt(3))/(3)` ...(Dividing by 2)
∴ x = `(9 + sqrt(3))/(3), (9 - sqrt(3))/(3)`
= `3 + sqrt(3)/(3), 3 - sqrt(3)/(3)`
= `3 + (1)/sqrt(3), 3 - (1)/sqrt(3)`.
APPEARS IN
RELATED QUESTIONS
Represent the following situation in the form of a quadratic equation.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Solve the equation `2x - 1/x = 7`. Write your answer correct to two decimal places.
Solve: x4 – 2x² – 3 = 0.
Without solving, comment upon the nature of roots of the following equation:
`x^2 + 2sqrt(3)x - 9 = 0`
`x^2+12x+35=0`
`4sqrt6x^2-13x-2sqrt6=0`
`x^2-(2b-1)x+(b^2-b-20)=0`
Solve:
`2((2x - 1)/(x + 3)) - 3((x + 3)/(2x - 1)) = 5; x ≠ -3, (1)/(2)`
The value (values) of x satisfying the equation x2 – 6x – 16 = 0 is ______.
If 3x2 – kx – 15 = (3x – 5)(x + 3), the value of k is ______.
