If-2x-a-n-a-n-and-2y-a-n-a-n-calculate-the-value-of-x-2-y-2-in-its-simplest-form-

Question Number 113451 by pete last updated on 13/Sep/20

If 2 x = a^{n} + a^{- n} and 2 y = a^{n} - a^{- n} calculate

the value of x^{2} - y^{2} in its simplest form

Answered by bemath last updated on 13/Sep/20

4 x^{2} = a^{2 n} + a^{- 2 n} + 2

4 y^{2} = a^{2 n} + a^{- 2 n} - 2

\Rightarrow 4 x^{2} - 4 y^{2} = 4

\Rightarrow x^{2} - y^{2} = 1

Answered by Her_Majesty last updated on 13/Sep/20

2 x = 2 c o s h (n l n a)

2 y = 2 s i n h (n l n a)

x^{2} - y^{2} = 1

Commented by Her_Majesty last updated on 13/Sep/20

{y o u}^{'} r e w r o n g .

2 x = a^{n} + a^{- n} = e^{n l n a} + e^{- n l n a} = 2 \times (e^{n l n a} + e^{- n l n a}) / 2 =

= 2 c o s h (n l n a)

s i m i l a r 2 y = 2 s i n h (n l n a)

{c o s h}^{2} θ - {s i n h}^{2} θ = 1

Answered by MJS_new last updated on 13/Sep/20

\frac{{(u + v)}^{2}}{4} - \frac{{(u - v)}^{2}}{4} = u v

h e r e v = \frac{1}{u} \Rightarrow u v = 1

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