Find the value of n∈N such that the curve (ax)n+(by)n=2 touches the straight line ax+by=2 at the point (a,b)˙

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Find the value of {n}{N} such that the curve {({{x}}{{a}})}^{{

Question

Find the value of $n \in N$ such that the curve $(\frac{x}{a})^{n} + (\frac{y}{b})^{n} = 2$ touches the straight line $\frac{x}{a} + \frac{y}{b} = 2$ at the point $(a, b) ˙$

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Benjamin Discussed

Find the value of

n \in N

such that the curve

(\frac{x}{a})^{n} + (\frac{y}{b})^{n} = 2

touches the straight line

\frac{x}{a} + \frac{y}{b} = 2

at the point

(a, b) ˙

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Question Text

Find the value of

n \in N

such that the curve

(\frac{x}{a})^{n} + (\frac{y}{b})^{n} = 2

touches the straight line

\frac{x}{a} + \frac{y}{b} = 2

at the point

(a, b) ˙