(3)

Sol. |  nx| = px

It is sufficient to find values of p for which y = |  nx| and y = px has three points in common.

If y = px is passing through points O, A, B then we obtain three roots.

Let us consider line y = px. When it is passing through points O, P. (tangent)

Let P ( α , p α ) ( α > 1)

⇒ p α = |  n α |

p α =  n α .....(1)

p = .....(2)

(1) , (2) ⇒ α = e

Slope of tangent (OP) is .

For three roots condition is 0 < p < .

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