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If 3x-2y=11 and x y=12 , find the value ...

If `3x-2y=11` and `x y=12` , find the value of `27\ x^3-8y^3`

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To find the value of \( 27x^3 - 8y^3 \) given the equations \( 3x - 2y = 11 \) and \( xy = 12 \), we can follow these steps: ### Step 1: Cube the equation \( 3x - 2y = 11 \) We start by cubing both sides of the equation: \[ (3x - 2y)^3 = 11^3 \] ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x^2+1/(x^2)=98 , find the value of x^3+1/(x^3)

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  2. If 2x+3y=13 and x y=6 , find the value of 8x^3+27\ y^3

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  3. If 3x-2y=11 and x y=12 , find the value of 27\ x^3-8y^3

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  4. If x^4+1/(x^4)=119 , find the value of x^3-1/(x^3)

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  5. Evaluate each of the following: (103)^3 (ii) (98)^3 (iii) (9. 9)...

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  6. Evaluate each of the following: (10. 4)^3 (ii) (598)^3 (iii) (99...

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  7. Evaluate each of the following: (i)111^3-\ 89^3 (ii) 46^3+34^3

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  8. Evaluate each of the following: (i)104^3+\ 96^3 (ii) 93^3-\ 107^3

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  9. If x+1/x=3, calculate x^2+1/(x^2),\ x^3+1/(x^3) and x^4+1/(x^4)

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  10. If x^4+1/(x^4)=194 ,\ find x^3+1/(x^3),\ x^2+1/(x^2) and x+1/x

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  11. Find the value of 27 x^3+\ 8y^3, if (i)3x+2y=14 and x y=8 (ii)3x+2y=2...

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  12. Find the value of 64 x^3-\ 125 z^3, if 4x-5z=16 and x z=12

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

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  14. Find the products: (x+3y)(x^2-\ 3x y+9y^2)

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  15. Find the products: (7a-5b)(49 a^2+35 a b+25 b^2)

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  16. Find the product: (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+0.49 y^2)

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  17. Find the following products: (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+0. 4...

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

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  19. Simplify: (6m-n)(36 m^2+6m m+n^2)-(3m+2n)^3

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

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