1.

य‌द‌ि `a+b+c,a^(2)+b^(2)=c^(2)=14` और `a^(3)+b^(3)+c^(3)=36` है तो `abc` का मान क्या होगा?A. 3B. 6C. 9D. 12

Answer» Correct Answer - B
`a+b+c=6`
`=a^(2)+b^(3)+c^(3)=36`
Put values as
`a=1, b=1, c=3`
`1+2+3=6`
`1+4+9=14`
`1+8+27=36`
`:. abc=1xx2xx3=6`
Alternate:
`:.(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2(ab+bc+ca)`
`36=14+2(ab+bc+ca)`
`(ab+bc+ca)=11`
`impliesa^(3)+b^(3)+c^(3)-3abc=(a+b+c)`
`(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`implies 36-3abc=6(14-11)`
`implies 36-3abc=6xx3`
`-3abc=18-36`
`3abc=18`
`abc=6`


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