Find the value of x if 2x + 1, x2 + x +1, 3x2 - 3x +3 are consecutive terms of an ap
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Answer:Sol : a, b, c are in A.P 2b = a + c Given that 2x + 1, x2 + x + 1, 3x2 - 3x + 3 are consecutive terms of an AP 2(x2 + x + 1) = 2x + 1 + 3x2 - 3x + 3 2x2 + 2x + 2 = 3x2 - x + 4. x2 - 3x + 2 = 0 x2 - 2x - x + 2 = 0 x(x - 2) -1(x - 2) = 0 x -1 = 0 ,x - 2 = 0 x = 1
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x=1
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Answer:Sol : a, b, c are in A.P 2b = a + c Given that 2x + 1, x2 + x + 1, 3x2 - 3x + 3 are consecutive terms of an AP 2(x2 + x + 1) = 2x + 1 + 3x2 - 3x + 3 2x2 + 2x + 2 = 3x2 - x + 4. x2 - 3x + 2 = 0 x2 - 2x - x + 2 = 0 x(x - 2) -1(x - 2) = 0 x -1 = 0 ,x - 2 = 0 x = 1
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