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प्रश्न
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
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उत्तर
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
`(("x" -3)("x" - 4) + ("x" - 1)("x" - 4) + ("x" - 1)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`("x"^2 - 3"x" - 4"x" + 12 + "x"^2 - "x" - 4"x" + 4 + "x"^2 - "x" - 2"x" + 2)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3"x"^2 - 15 "x" + 18)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3("x"^2 - 5"x" + 6))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3("x" - 3)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`3/(("x" - 1)("x" - 4)) = 1/6`
x2 - 5x+ 4= 18
x2 - 5x - 14= 0
x2 + 2x - 7x -14= 0
x( x+ 2) - 7(x + 2)= 0
(x + 2)(x - 7) = 0
x = -2, x = 7
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