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if a-b=6 , ab=20 . find a^3-b^3...

if a-b=6 , ab=20 . find `a^3-b^3 `

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To solve the problem where \( a - b = 6 \) and \( ab = 20 \), we need to find \( a^3 - b^3 \). We can use the algebraic identity for the difference of cubes: \[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \] ### Step 1: Identify the values we have We know: ...
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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. If a^2+b^2+c^2-a b-b c-c a=0, then find the relation between a,b and c

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  2. If 9x^2+25 y^2=181 and x y=-6, find the value of 3x+5y

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  3. if a-b=6 , ab=20 . find a^3-b^3

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  4. Write the following in expanded form: (i)(9x+2y+z)^2 (ii) (3x+2y...

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

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  7. Simplify : (i)(a+b+c)^2 (ii) (a+b+c)^2-(a-b-c)^2

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

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

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

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

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

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

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

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

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  17. 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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  18. Without actually calculating the cubes. Find the value of each of th...

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  19. If a+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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  20. If x-1/x=3+2sqrt(2) , find the value of x^3-1/(x^3)

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