Question

If the lines x —y = a and x + y = b ar3 tangents for y = x2 — 3x +2 then a/b =

Answer 1

It has given that, the lines x - y = a and x + y = b are tangents for y = x² - 3x + 2.

To find : The value of a/b

solution : equation of curve is y = x² - 3x + 2

differentiating with respect to x we get,

slope of tangent of curve = dy/dx = 2x - 3

but two tangents of given curve is x - y = a and x + y = b

slope of 1st tangent = 1

slope of 2nd tangent = -1

case 1 : dy/dx = 1 = 2x - 3

⇒x = 2 and then y = (2)² - 3(2) + 2 = 0

so, (2, 0) putting it in equation x - y = a

so, 2 - 0 = a ⇒a = 2

case 2 : dy/dx = -1 = 2x - 3

⇒x = 1 and then y = (1)² - 3(1) + 2 = 0

so, (1, 0) lies on equation x + y = b

so, 1 + 0 = b ⇒b = 1

now the value of a/b = 2/1 = 2

Answer 2

Step-by-step explanation:

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