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1/x-1,1/x-2,1/x-5is an ap so find value of x =? |
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Answer» x= -2,1Step-by-step explanation:Given:a₁ = 1/x-1a₂ = 1/x-2a₃ = 1/x-5As we know that, if a series is and an ap, then it must have a common difference.∴a₂ - a₁ = a₃ - a₂ ⇒ 1/x-2 - 1/x-1 = 1/x-5 - 1/x-2⇒ x-1 -x+2/(x-2) (x-1) = x-2 - x+5/(x-5) (x-2)⇒ 1/x²-x-2x+2 = 3/x²-2x-5x+10By cross multiplication,x²-2x-5x+10 = 3 (x²-x-2x+2)⇒ x²-7x+10 = 3x²-9x+6⇒ x²-3x²-7x+9x+10-6 = 0⇒ -2x²-2x+4 = 0⇒ -2(x²+x-2) = 0⇒ x²+x-2 = 0By MIDDLE term or you can USE any factorizing methodx²-x+2x-2 = 0⇒ x(x-1)+2(x-1) = 0⇒ (x+2) (x-1) = 0Now, x²+x-2 this term has TWO heroes ∴ x+2 = 0⇒ x = -2x-1 = 0⇒ x = 1Therefor both numbers can be there, or you can find it by substituting the numbers ONE by one in the ap. |
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