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Question Number 87464 by jagoll last updated on 04/Apr/20

$$\mathrm{x}+\sqrt{\mathrm{y}}=7$$$$\sqrt{\mathrm{x}}+\mathrm{y}=11$$$$\mathrm{find}\mathrm{x}\mathrm{and}\mathrm{y}$$

Commented by john santu last updated on 04/Apr/20

$$\mathrm{y}=9\wedge \mathrm{x}=4$$

Commented by john santu last updated on 05/Apr/20

$$\sqrt{\mathrm{y}}=7-\mathrm{x}$$$$\mathrm{y}=49-14\mathrm{x}+{\mathrm{x}}^2$$$$11-\sqrt{\mathrm{x}}=49-14\mathrm{x}+{\mathrm{x}}^2$$$${\mathrm{x}}^2-14\mathrm{x}+\sqrt{\mathrm{x}}+38=0$$$$[\sqrt{\mathrm{x}}=\mathrm{w}]$$$${\mathrm{w}}^4-{14\mathrm{w}}^2+\mathrm{w}+38=0$$$$(\mathrm{w}-2)({\mathrm{w}}^3+{2\mathrm{w}}^2-10\mathrm{w}-19)=0$$$$\mathrm{w}=2=\sqrt{\mathrm{x}}\Rightarrow \mathrm{x}=4$$$$\Rightarrow \sqrt{\mathrm{y}}=7-4=3\Rightarrow \mathrm{y}=9$$

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