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Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c ...

Prove that: `2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]`

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"LHS`= 2a^2+2b^2+2c^2-2ab-2bc-2ca`
`=(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)`
`=[(a-b)^2+(b-c)^2+(c-a)^2]`
`=RHS` "
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If 3x+2y=12 and x y=6 , find the value of 9x^2+4y^2

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

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  3. Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

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  4. If : a^2+b^2+c^2-a b-b c-c a=0 , prove that a=b=c

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  5. Evaluate each of the following using identities: (i)(2x-1/x)^2 (ii...

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  6. Evaluate each of the following using identities: (a^2b-b^2a)^2 (ii)...

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  7. Evaluate each of the following using identities: (1. 5 x^2-0. 3 y^2) ...

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  8. Evaluate each of the following using identities: (i)(399)^2(ii) (0. 98...

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  9. Evaluate each of the following using identities: (i)991 xx 1009 (ii) 1...

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  10. Simplify each of the following: 175 xx 175+2 xx 175 xx 25+25 xx 25

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  11. Simplify each of the following: 322 × 322−2 × 322 × 22+22 × 22

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  12. Simplify each of the following: 0. 76 xx 0. 76+2xx 0. 76 xx 0. 24+0. 2...

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  13. Simplify each of the following: (7. 83 xx 7. 83-1. 17 xx 1. 17)/(6. 66...

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  14. If x+1/x=11 , find the value of x^2+1/(x^2)

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

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  16. If x+1/x=sqrt(5) , find the values of x^2+1/(x^2) and x^4+1/(x^4)

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  17. If x^2+1/(x^2)=66 , find the value of x-1/x

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  18. If x^2+1/(x^2)=79 , find the value of x+1/x

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  19. If 9x^2+25 y^2=181\ \ a n d\ x y\ =\ -6, find the value of 3x+5y

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  20. If 2x+3y=8 and x y=2 , find the value of 4x^2+9y^2

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