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Prove that a^2+b^2+c^2-a b-b c-c a is al...

Prove that `a^2+b^2+c^2-a b-b c-c a` is always non-negative for all values of `a ,b and `c` cdot`

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To prove that the expression \( a^2 + b^2 + c^2 - ab - ac - bc \) is always non-negative for all values of \( a, b, \) and \( c \), we can follow these steps: ### Step 1: Rewrite the Expression We start with the expression: \[ E = a^2 + b^2 + c^2 - ab - ac - bc \] ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. if a-b=6 , ab=20 . find a^3-b^3

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  2. Write the following in expanded form: (9x+2y+z)^2

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  3. Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all valu...

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  4. If a+b+c=9 and a b+b c+c a=40 , find a^2+b^2+c^2dot

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  5. Simplify : (a+b+c)^2

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  6. If x^2+1/(x^2)=98 , find the value of x^3+1//x^3

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  7. Simplify the following: 7x^3+8y^3-(4x+3y)(16 x^2-12 x y+9y^2)

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  8. If a-b=6 and a b=20 , find the value of a^3-b^3

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  9. If a+b=10 and a b=21 , find the value of a^3+b^3

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  10. If 4x^2+y^2=40 and x y=6, find the value of 2x+ydot

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  11. If a+b=7 and a b=12 , find the value of (a^2-a b+b^2)

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  12. If x^2+1/(x^2)=83. find the value of x^3-1//x^3

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  13. If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3d...

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  14. Find the following products: (i) (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+0...

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  15. If a+b+c=15 and a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3abc

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  16. Without actually calculating the cubes. Find the value of each of t...

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  17. Ifa +b+c=9 and a^2+b^2+c^2=35 , find the value of a^3+b^3+c^3-3a b c

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  18. If x-1/x=3+2sqrt(2) , find the value of x^3-1/(x^3)

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  19. If x+y=12 and x y=32 , find the value of x^2+y^2dot

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  20. If 3x+2y=12 and x y=6, find the value of 9x^2+4y^2 (3x+2y)^2=9x^2+4y...

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