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Question Number 140273 by liberty last updated on 06/May/21

$$2\sqrt{\mathrm{x}-1}+5\mathrm{x}=\sqrt{({\mathrm{x}}^2+4)(\mathrm{x}+24)}$$

Answered by MJS_new last updated on 06/May/21

$$x=5$$$$\mathrm{I}\mathrm{saw}\mathrm{that}(5^2+4)(5+24)={29}^2$$$$$$$$f\left(x\right)=5x+2\sqrt{x-1}-\sqrt{(x^2+4)(x+24)}$$$$\frac{df}{dx}=0$$$$5+\frac{1}{\sqrt{x-1}}-\frac{3x^2+48x+4}{2\sqrt{(x^2+4)(x+24)}}=0$$$$\Rightarrow x=5\Rightarrow \mathrm{maximum}\mathrm{at}x=5\Rightarrow \mathrm{no}\mathrm{other}\mathrm{solution}$$

Answered by liberty last updated on 06/May/21

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