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Question Number 137594 by Ñï= last updated on 04/Apr/21

$$(x+\sqrt{x^2+1})(y+\sqrt{y^4+4})=9$$$$x\sqrt{y^4+4}+y\sqrt{x^2+1}=?$$

Answered by bemath last updated on 04/Apr/21

$$letx=\tan t\wedge y=2\tan z$$$$\Rightarrow (\tan t+\sec t)(2\tan z+2\sec z)=9$$$$(\tan t+\sec t)(\tan z+\sec z)=\frac{9}{2}$$$$\iff \tan t.\tan z+\tan t.\sec z+\sec t.\tan z+\sec t.\sec z=\frac{9}{2}$$$$\Rightarrow \tan t.2\sec z+2\tan z.\sec t=x$$$$\Rightarrow \tan t.\sec z+\tan z.\sec t=\frac{x}{2}$$$$$$

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