If the tangent to the curve y = x^ 3 - x^ 2 + x at the point (a, b) is also tangent to the curve y = 5x^ 2 + 2x - 25 at the point (2, −1), then |2a + 9b| is equal to _____.

JEE Main 2022 Mathematics question

If the tangent to the curve at the point (a, b) is also tangent to the curve at the point (2, −1), then |2a + 9b| is equal to .

Answer: 195

For the slope at (2, −1) is 10(2) + 2 = 22, so the tangent is y + 1 = 22(x − 2), i.e. y = 22x − 45. For the slope at (a, b) is , so ,

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Question ID VK-035072