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If x=(b-c)(a-d),y=(c-a)(b-d),z=(a-b)(c-d...

If `x=(b-c)(a-d),y=(c-a)(b-d),z=(a-b)(c-d)`, then the what is `x^(3)+y^(3)+z^(3)` equal to?

A

xyz

B

2xyz

C

3xyz

D

`-3xyz`

Text Solution

Verified by Experts

The correct Answer is:
C
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LUCENT PUBLICATION-ALGEBRAIC IDENTITIES -Exercise - 1A
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  2. If x varies as m^(th) power of y, y varies as n^(th) power of z and x ...

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  3. If x=(b-c)(a-d),y=(c-a)(b-d),z=(a-b)(c-d), then the what is x^(3)+y^(3...

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  4. If a+b+c=6, a^(2)+b^(2)+c^(2)=26, then ab+bc+ca is equal to

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  5. If 3x^(3) -2x^(2)y -13xy^(2)+10y^(3) is divided by x-2y, then what wil...

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  6. If (a+(1)/(a))^(2)=3 then what is the value of 1+a^(6)+a^(12) +a^(18) ...

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  7. IF x+y+z=0 then what is (xyz)/((x+y)(y+z)(z+x)) equal to

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  8. IF (5x-7y+10)/1=(3x+2y+1)/8=(11x+4y-10)/9 then what is x+y equal to

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  9. If ( 2x - 3y + 1)/(2) = (x + 4y + 8)/(3) = ( 4x - 7y + 2)/(5) then wh...

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  10. If x = a ( b - c) , y = b ( c - a) and z = c ( a - b) then ((x)/...

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  11. If x^2 + 2 = 2 x , then the value of x^4 - x^3 - x^2 + 2 is

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  12. If 2^(x)=3^(y)=6^(-z), then the value of 1/x+1/y+1/z-

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  13. If (1)/( x + y) = (1)/(x) + (1)/(y) ( x ne 0, y ne 0, x ne y) then t...

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  14. For real a, b, c if a^(2) + b^(2) + c^(2)= ab + bc + ca then value ...

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  15. If x+(1)/(x)=5 then (2x)/(3x^(2)-5x+3) is

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  16. If x^(4) +(1)/(x^(4)) =119 and x gt 1 then what is the value of x^(3)-...

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  17. If (x+y-z)^(2) +(y+z-x)^(2) +(z+x-y)^(2)=0 then what is the value o...

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  18. If x - y = ( x + y)/(7) = (xy)/(4) the numerical value of xy is

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  19. If x + y + z = 0 then (x^(2))/(yz) + (y^(2))/( zx)+ ( z^(2))/( xy)=...

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  20. If x + y = a and xy = b^(2) then the value of x^(3) - x^(2) y - x...

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