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If a+b+c=9 and ab + bc + ca = 26, find a...

If a+b+c=9 and ab + bc + ca = 26, find `a^2 + b^2 +c^2.`

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VGS PUBLICATION-BRILLIANT-POLYNOMIAL AND FACTORIISATION-EXERCISE
  1. Factorise : 25x^2 + 16y^2 + 42^2 - 40xy + 16yz -20xz.

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  2. Factorise : 9a^2 + 4b^2+ 16c^2+12ab16bc -24ca.

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  3. If a+b+c=9 and ab + bc + ca = 26, find a^2 + b^2 +c^2.

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  4. Evaluate the following using suitable identities : (99)^3.

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  5. Evaluate the following using suitable identities : (102)^3.

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  6. Evaluate the following using suitable identities : (998)^3.

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  7. Evaluate the following using suitable identities : (1001)^3.

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  8. Factorise of the following. : 8a^3+b^3+12a^2b^2 + 6ab^2.

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  9. Factorise of the following : 8a^3-b^3-12a^2b + 6ab^2.

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  10. Factorise of the following : 1-64a^3-12a + 48a^2.

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  11. Factorise of the following : 8p^3-12/5p^2+6/25p -1/125.

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  12. Verify : x^3 + y^3 = (x + y) (x^2- xy + y^2)

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  13. Verify x^3-y^3=(x-y)(x^2+xy+y^2) Using some non-zero positive integers...

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  14. Factorise : 27a^3 + 64b^3.

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  15. Factorise : 343y^3 - 1000.

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  16. Factorise : 27x^3+y^3+z^3-9xyz using identity.

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  17. x^(3)+y^(3)+z^(3)-3xyz = 1/2 (x+y+z) [(x-y)^(2)+(y-z)^(2)+(z-x)^(2)] స...

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  18. x+y+z=0 అయితే x^(3)+y^(3)+z^(3)=3xyz అని నిరూపించండి.

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  19. Show that (a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)

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  20. Without actual calculating the cubes, find the value of the following ...

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