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Question Number 106663 by I want to learn more last updated on 06/Aug/20

Answered by Her_Majesty last updated on 06/Aug/20

$$\frac{y}{6}=\frac{6}{x}\Rightarrow y=\frac{36}{x}$$$${(x+6)}^2+{(y+6)}^2={20}^2$$$$\Rightarrow$$$$x^4+12x^3-328x^2+432x+1296=0$$$$(x^2+(6-2\sqrt{109})x+36)(x^2+(6+2\sqrt{109})x+36)=0$$$$x>0$$$$\Rightarrow$$$$x=-3+\sqrt{109}\pm \sqrt{82-6\sqrt{109}}$$$$x>y$$$$\Rightarrow$$$$x=-3+\sqrt{109}+\sqrt{82-6\sqrt{109}}$$$$y=-3+\sqrt{109}-\sqrt{82-6\sqrt{109}}$$

Answered by Aziztisffola last updated on 06/Aug/20

$$\mathrm{solve}$$$$\frac{\mathrm{x}}{\mathrm{x}+6}=\frac{6}{\mathrm{y}+6}=\frac{{\mathrm{x}}^2+36}{20}$$$$\frac{\mathrm{x}}{\mathrm{x}+6}=\frac{6}{\mathrm{y}+6}\iff 6(\mathrm{x}+6)=\mathrm{x}(\mathrm{y}+6)$$$$\iff \mathrm{y}=\frac{36}{\mathrm{x}}\mathrm{and}\mathrm{x}>0.$$$$$$

Commented by prakash jain last updated on 06/Aug/20

$$\mathrm{Use}+\mathrm{button}\mathrm{at}\mathrm{top}\mathrm{to}\mathrm{add}\mathrm{a}\mathrm{new}$$$$\mathrm{question}$$

Commented by Aziztisffola last updated on 06/Aug/20

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{just}\mathrm{a}\mathrm{part}\mathrm{of}\mathrm{answer}\mathrm{sir}{\mathrm{isn}}^{\prime }\mathrm{t}\mathrm{a}\mathrm{new}\mathrm{topic}.$$

Commented by prakash jain last updated on 06/Aug/20

$$\mathrm{Ok}.\mathrm{I}\mathrm{see}\mathrm{now}\mathrm{my}\mathrm{mistake}.\mathrm{Sorry}.$$

Commented by Aziztisffola last updated on 06/Aug/20

$$\mathrm{no}\mathrm{problem}\mathrm{sir}$$

Commented by I want to learn more last updated on 06/Aug/20

$$\mathrm{How}\mathrm{do}\mathrm{you}\mathrm{get}\mathrm{the}\mathrm{equation}\mathrm{sir}?$$

Commented by Her_Majesty last updated on 06/Aug/20

$$butyouseeIfoundapositivesolution?$$$$so{where}^{\prime }stheerror?oneofusmustbe$$$$wrongatleast...$$

Commented by Aziztisffola last updated on 06/Aug/20

$$\mathrm{Thales}\mathrm{and}\mathrm{pythagor}\mathrm{theorem}.$$

Commented by Her_Majesty last updated on 06/Aug/20

$${\mathrm{x}}^3+{6\mathrm{x}}^2+16\mathrm{x}+216=0$$$$hasonly1realsolutionx\approx -7.62$$

Commented by Aziztisffola last updated on 06/Aug/20

$$\mathrm{yes}\mathrm{sir},{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{have}\mathrm{no}\mathrm{positive}\mathrm{solution}$$

Commented by Aziztisffola last updated on 11/Aug/20

$$\mathrm{this}\mathrm{equation}{(\mathrm{x}+6)}^2+{(\mathrm{y}+6)}^2=400$$$$\mathrm{have}\mathrm{two}\mathrm{solutions}\mathrm{one}\mathrm{of}\mathrm{them}\left(\mathrm{positive}\right)\mathrm{is}\mathrm{the}$$$$\mathrm{answer}\mathrm{of}\mathrm{problem}.$$

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