[HSG] Đại 9

N

nhuquynhdat

$xy + \sqrt{(1 + x^2)(1 + y^2)} = a$

$\leftrightarrow [xy + \sqrt{(1 + x^2)(1 + y^2)}]^2=a^2$

$\leftrightarrow x^2y^2+(1+x^2)(1+y^2)+2xy \sqrt{(1+x^2)(1+y^2)} =a^2$

$\leftrightarrow x^2+y^2+2x^2y^2+1+2xy \sqrt{(1+x^2)(1+y^2)}=a^2$

$\leftrightarrow x^2+y^2+2x^2y^2+2xy \sqrt{(1+x^2)(1+y^2)}=a^2-1$

$S^2= x^2+y^2+2x^2y^2+2xy \sqrt{(1+x^2)(1+y^2)} =a^2-1$

$\Longrightarrow S= \sqrt{a^2-1}$
 
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