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If a^2+b^2+c^2=20\ \ a n d\ a+b+c=0, fin...

If `a^2+b^2+c^2=20\ \ a n d\ a+b+c=0,` find `a b+b c+c a`

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To solve the problem, we need to find the value of \( ab + bc + ca \) given that \( a^2 + b^2 + c^2 = 20 \) and \( a + b + c = 0 \). ### Step-by-Step Solution: 1. **Start with the given equations:** \[ a + b + c = 0 \] ...
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Given, a^(2) =b+c, b^(2)=c + a " & " c^(2) = a + b or (a^(2))/(b+c) = (b^(2))/(c+a) = (c^(2))/(a+b)=1 find (a)/(1+a) + (b)/(1+b) + (c )/(1+c) = ?

RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Factorize: x^2-1-2a-a^2

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  2. If a+b+c=0, then write the value of a^3+b^3+c^3

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  3. If a^2+b^2+c^2=20\ \ a n d\ a+b+c=0, find a b+b c+c a

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

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

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  6. Write the value of 25^3-75^3+50^3,If a+b+c=0

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  7. Write the value of 48^3-30^3-18^3

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  8. Write the value of (1/2)^3+(1/3)^3-\ (5/6)^3

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  9. Write the value of 30^3+20^3-50^3

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  10. The factors of a^2-1-2x-x^2 are (a)(a-x+1)(a-x-1) (b)(a+x-1)(a-x+1) (c...

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  11. The factors of x^4+x^2+25 are (a)(x^2+3x+5)(x^2-3x+5) (b)(x^2+3x+5)(x...

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  12. The factors of x^2+4y^2+4y-4x y-2x-8 are (a)(x-2y-4)(x-2y+2) (b) (x-y...

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  13. The factors of x^3-x^2y-x y^2+y^3 are (a(x+y)(x^2-x y+y^2) (b) (x+y...

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  14. The factors of x^3-1+y^3+3x y are (a) (x-1+y)(x^2+1+y^2+x+y-x y) (b)...

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  15. The factors of 8a^3+b^3-6a b+1 are (a) (2a+b-1)(4a^2+b^2+1-3a b-2a) ...

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  16. (x+y)^3−(x−y)^3 can be factorized as  (a) 2y(3x^2+y^2) (b) 2x(3x^2+y...

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  17. The factors of x^3-7x+6 are

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  18. The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a)(a-...

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  19. The expression x^4+4 can be factorized as (a) (x^2+2x+2)(x^2-2x+2) (...

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  20. If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x...

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