If the tangent to the curve y=x³-x²+x at the point (a, b) is also tangent to the curve y = 5x² + 2x - 25 at the point (2, - 1), then |2a + 9b| is equal to _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Evening shift · Q22

JEE Main 202229 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

If the tangent to the curve

y=x^{3}-x^{2}+x

at the point

(a, b)

is also tangent to the curve

y = 5{x^2} + 2x - 25

at the point (2,

-

1), then

|2a + 9b|

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.