InterviewSolution
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InterviewSolution
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`x+y+z=1, 1/x+1/y+1/z=1` और `xyz=-1` तो `x^(3)+y^(3)+z^(3)` का मान क्या है?A. -1B. 1C. -2D. 2 |
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Answer» Correct Answer - B `1/x+1/y+1/z=1` `(xy+yz+zx)/(xyz)=1` `=xy+yz+zx=xyz=-1` `(x+y+z)^(2)=x^(2)+y^(2)+z^(2)+2(xy+yz+zx)` `(x+y+z)^(2)=x^(2)+y^(2)+z^(2)+2(xy+yz+zx)` `(1)^(2)=x^(2)+y^(2)+z^(2)+2(-1)` `x^(2)+y^(2)+z^(2)=3` `x^(3)+y^(3)+z^(3)-3xyz` `=(x+y+z)[x^(2)+y^(2)+z^(2)-(xy+yx` `+zx]` `x^(3)+y^(3)+z^(3)-3(-1)=1[3-(-1)]` `x^(3)+y^(3)+z^(3)=4-3=1` |
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