AvgStudent
Full Member
- Joined
- Jan 1, 2022
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- 256
Problem:
Find the value of [imath]x+y[/imath], given:
[imath]x\sqrt{y}+y\sqrt{x}=182\\ x\sqrt{x}+y\sqrt{y}=183\\[/imath]
My attempt:
Adding equations 1 and 2, collect like terms and factor give:
[math]x\sqrt{y}+y\sqrt{x}+x\sqrt{x}+y\sqrt{y}=365\\ x\sqrt{y}+x\sqrt{x}+y\sqrt{x}+y\sqrt{y}=365\\ x(\sqrt{y}+\sqrt{x})+y(\sqrt{x}+\sqrt{y})=365\\ (x+y)(\sqrt{x}+\sqrt{y})=365[/math]
I'm not sure how to continue from here.
Find the value of [imath]x+y[/imath], given:
[imath]x\sqrt{y}+y\sqrt{x}=182\\ x\sqrt{x}+y\sqrt{y}=183\\[/imath]
My attempt:
Adding equations 1 and 2, collect like terms and factor give:
[math]x\sqrt{y}+y\sqrt{x}+x\sqrt{x}+y\sqrt{y}=365\\ x\sqrt{y}+x\sqrt{x}+y\sqrt{x}+y\sqrt{y}=365\\ x(\sqrt{y}+\sqrt{x})+y(\sqrt{x}+\sqrt{y})=365\\ (x+y)(\sqrt{x}+\sqrt{y})=365[/math]
I'm not sure how to continue from here.