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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^2` Given:

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Given:
`a+b+c=9`
`ab+bc+ca=40`
`(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)`
`9^2=a^2+b^2+c^2+2×40`
`81=a^2+b^2+c^2+80`
`a^2+b^2+c^2=1`
`therefore a^2+b^2+c^2=1`
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. Simplify: (a+b+c)^2-(a-b-c)^2

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  2. If a^2+b^2+c^2=20 and a+b+c=0 , find a b+b c+c a

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

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  4. If a^2+b^2+c^2=250 and a b+b c+c a=3 , find a+b+c ​

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  5. Write the following in the expanded form: (a+2b+c)^2 (ii) (2a-3b-c)...

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  6. Write the following in the expanded form: (-3x+y+z)^2 (ii) (m+2n-5p...

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  7. Write the following in the expanded form: (2+x-2y)^2 (ii) (a^2+b^2+...

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  8. Write the following in the expanded form: (a b+b c+c a)^2 (ii) (x/y...

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  9. Write the following in the expanded form: (a/(b c)+b/(c a)+c/(a b))^2 ...

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  10. Write the following in the expanded form: (2x-y+z)^2 (ii) (-2x+3y+2...

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  11. Simplify: (a+b+c)^2+\ \ (a-b+c)^2

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  12. Simplify: (a+b+c)^2-\ (a-b+c)^2

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  13. Simplify: (a+b+c)^2+\ (a-b+c)^2+\ (a+b-c)^2

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  14. Simplify: (2x+p-c)^2-\ (2x-p+c)^2

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  15. Simplify: (x^2+y^2-z^2)^2-\ \ (x^2-y^2+z^2)^2

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  16. If a+b+c=0 and a^2+b^2+c^2=16 , find the value of a b+b c+c a

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  17. If a^2+b^2+c^2=16 and a b+b c+c a=10 , find the value of a+b+c

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  18. If a+b+c=9 and a b+b c+c a=23 , find the value of a^2+b^2+c^2

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  19. Find the value of 4x^2+y^2+25 z^2+4x y-10 y z-20 z x when x=4,\ y=3 an...

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  20. Simplify : (x+y+z)^2+(x+y/2+z/3)^2-(x/2+y/3+z/4)^2 ​ ​

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