1.

यदि `x+y=4, x^(2)+y^(2)=14` और `xgty`, तो `x` और `y` का सही मान क्या होगा?A. `2-sqrt(2),sqrt(3)`B. `3,1`C. `2+sqrt(3),2-sqrt(3)`D. `2+sqrt(3),2sqrt(2)`

Answer» Correct Answer - C
`x^(2)+y^(2)=14`
`x+y=4`…………..i
Squaring both sides
`x^(2)+y^(2)+2xy=16`
`14+2xy=16`
`2xy=2`
`xy=1`
`x^(2)+y^(2)=14`
Substracting `(2xy)` from both sides
`x^(2)+y^(2)-2xy=14-2xy`
`(x-y)^(2)=14-2xx1`
`x=y=sqrt(12)`
`x-y=2sqrt(3)`..............ii
`y=2-sqrt(3)`
`x=2+sqrt(3)`


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