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If 3x+2y=12 and x y=6 , find the value o...

If `3x+2y=12` and `x y=6` , find the value of `9x^2+4y^2`

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To solve the problem step by step, we will use the given equations and algebraic identities. ### Given: 1. \(3x + 2y = 12\) (Equation 1) 2. \(xy = 6\) (Equation 2) ### We need to find: The value of \(9x^2 + 4y^2\). ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x^2+1/(x^2)=27 , find the value of each of the following: x-1/x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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