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√x + y = 7√y + x =11 Find x and y |
| Answer» {tex}√x + y = 7 and √y + x =11{/tex}Now,\xa0{tex}√x=7-y{/tex}or,\xa0{tex}x=(7-y)^2{/tex}Putting the value into other equation,we get,{tex}√y+(7-y)^2=11{/tex}or,\xa0{tex}√y+49-14y+y^2=11{/tex}or,\xa0{tex}y^2-14y+√y+38=0{/tex}Let{tex}√y=m => y=m^2{/tex}Now,\xa0{tex}m^4-14m^2+m+38=0{/tex}or,\xa0{tex}(m-2)(m^3+2m^2-10m-19)=0{/tex}Therefore,{tex}m-2=0{/tex}or,\xa0{tex}m=2{/tex}As we know that,\xa0{tex}\\sqrt{y} =m{/tex}Then,\xa0{tex}√y=2{/tex}or,\xa0{tex}y=4{/tex}Also,\xa0{tex}√x=7-y{/tex}\xa0or,\xa0{tex}√x=7-4=3{/tex}or,\xa0{tex}x=9{/tex}\xa0\xa0 | |