Show-that-the-equation-sec-2-4xy-x-y-2-is-only-possible-when-x-y-

Question Number 37745 by kunal1234523 last updated on 17/Jun/18

Show that the equation \sec^{2} θ = \frac{4 x y}{{(x + y)}^{2}} is

only possible when x = y

Answered by math1967 last updated on 17/Jun/18

x, y r e a l ∴ {(x - y)}^{2} ⩾ 0

{(x + y)}^{2} - 4 x y ⩾ 0 \Rightarrow {(x + y)}^{2} ⩾ 4 x y

\Rightarrow 4 x y ⩽ {(x + y)}^{2}

\Rightarrow \frac{4 x y}{{(x + y)}^{2}} ⩽ 1 b u t {s e c}^{2} θ ⩾ 1

n o w i f x = y t h e n \frac{4 x y}{{(x + y)}^{2}} = 1

∴ \sec^{2} θ = \frac{4 x y}{{(x + y)}^{2}} i s p o s s i b l e w h e n x = y

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