If the lines x + y = a and x – y = b touch the curve y = x^(2) – 3x + 2 at the points where the curve intersects the x-axis, then a / b is equal to _______.

y = x^2 – 3x + 2 => y = (x – 1)(x – 2) At x-axis y = 0 => x = 1, 2 So this curve intersects the x-axis at A(1, 0) and B(2, 0). dy / dx = 2x - 3 ( dy / dx )_x = 1 = - 1 and ( dy / dx )_x = 2 = 1 Equation of tangent at A(1, 0) : y = –1(x –1) => x + y = 1 and equation of tangent at B(2, 0): y = 1(x – 2) => x – y = 2 So a = 1 and b = 2 => a / b = 0.5

If the lines x y a and x y b touch the curve y x2 3x 2 ... | null (Mathematics)

y = x^2 – 3x + 2

\Rightarrow y = (x – 1)(x – 2)

\text{ At } x\text{-axis } y = 0

\Rightarrow x = 1, 2

So this curve intersects the x-axis at A(1, 0) and B(2, 0).

{{dy} \over {dx}} = 2x - 3

{\left( {{{dy} \over {dx}}} \right)_{x = 1}} = - 1 \text{ and } {\left( {{{dy} \over {dx}}} \right)_{x = 2}} = 1

Equation of tangent at A(1, 0) :

y = –1(x –1)

\Rightarrow x + y = 1

and equation of tangent at B(2, 0):

y = 1(x – 2)

\Rightarrow x – y = 2

a = 1

and

b = 2

\Rightarrow {a \over b} = 0.5

Explanation

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