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The even solution of equation dy/dx=12 is the first term of an arithmetical sequence with common difference 4. Find a7 and a11. y=2x^3-3x^2

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We have y = 2x^3 - 3x^2.

The solution of dy/dx = 12 is the first term of the arithmetic sequence with common difference 4.

dy/dx = 12

=> 6x^2 - 6x = 12

=> x^2 - x = 2

=> x^2 - 2x + x - 2 = 0

=> x(x - 2) + 1(x - 2) = 0

=> (x + 1)(x - 2) = 0

The even root is 2.

The nth term of an arithmetic sequence is a + (n - 1)d

a = 2 , d = 4

a7 = 2  + 6*4 = 26

a11 = 2 + 10*4 = 42

The required terms: a7 = 26 and a11 = 42

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