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

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

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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. Write the following in expanded form: (i)(9x+2y+z)^2 (ii) (3x+2y...

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

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

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

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

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

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

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

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

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

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

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  14. 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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  15. Without actually calculating the cubes. Find the value of each of th...

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

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

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

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  20. If x+1/x=6 , find (i)x^2+1/(x^2) (ii) x^4+1/(x^4)

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