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If a+b+c=0 then prove the following. ...

If `a+b+c=0` then prove the following.
`(bc+ca+ab)^(2) =b^(2)c^(2) +c^(2)a^(2) +a^(2)b^(2)=(1)/(4) (a^(2) +b^(2) +c^(2))^(2)`

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LUCENT PUBLICATION-ALGEBRAIC IDENTITIES -Exercise - 1B
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  3. If x=(0.08)^(2), y=(1)/((0.08)^(2)) and z=(1-0.08)^(2)-1 then which of...

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  4. If x^(4)+(1)/(x^(4))=23 then what is the value of (x-(1)/(x))^(2)?

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  5. If x+(1)/(x)=3 then what is the value of x^(5)+(1)/(x^(5)) ?

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  6. If a+b=6, a-b=2 then what is the value of 2(a^(2)+b^(2))?

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  7. If 2a-(2)/(a)+3=0, then value of (a^(3)-(1)/(a^(3))+2) is -

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  8. If factors of x^(3)+(a+1) x^(2)-(b-2)x -6 are (x+1) and (x-2) then val...

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  9. If x is real and x^(4)+(1)/(x^(4))=119, then value of (x-(1)/(x)) is

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  10. If x^(3) + y^(3) = 35 and x + y = 5 then the value of (1)/( x) + (...

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  11. If (x^(2))/(by+cz)=(y^(2))/(cz+ax)=(z^(2))/(ax+by)=1, then value of (a...

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  12. Value of a and b(a gt 0, b lt 0) for which 8x^(3)-ax^(2)+54x+b is a pe...

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  13. If x = ( 4ab)/(a +b) ( a ne b) the value of ( x + 2a)/( x - 2a) + ( x...

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  14. If a+b+c=8, then value of (a-4)^(3) +(b-3)^(3) +(c-1)^(3)-3(a-4) (b-3)...

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  15. If x = sqrt(a) + (1)/( sqrt(a)) , y = sqrt(a) - (1)/( sqrt(a)) ( a gt...

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  16. If 5a+(1)/(3a)=5, then value of 9a^(2)+(1)/(25a^(2)) is

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  17. If a+b+c=0, then what is the value of a^(2)/(bc)+b^(2)/(ca)+c^(2)/(ab)...

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  18. If a, b, c are real, a^(3)+b^(3)+c^(3)=3abc and a+b+c ne 0, then relat...

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  19. If a^(2)+(1)/(a^(2))=98, a gt 0 , then the value of a^(3)+(1)/(a^(3)) ...

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  20. If x+(1)/(x)=5 then what is the value of (x^(4)+(1)/(x^(2)))/(x^(2)-3x...

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  21. If a ^(2) + b ^(2) + c ^(2) = 2 (a - b -c) - 3, then the value of 2a -...

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