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If (a-3)^(2)+(b-4)^(2) +(c-9)^(2)=0 then...

If `(a-3)^(2)+(b-4)^(2) +(c-9)^(2)=0` then what is the value of `sqrt(a+b+c)`?

A

`-4 `

B

4

C

`pm4 `

D

`pm 2`

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The correct Answer is:
To solve the equation \((a-3)^{2} + (b-4)^{2} + (c-9)^{2} = 0\), we will follow these steps: ### Step 1: Understand the equation The equation states that the sum of three squares is equal to zero. Since the square of any real number is non-negative, the only way for this sum to equal zero is if each individual square is also zero.
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LUCENT PUBLICATION-ALGEBRAIC IDENTITIES -Exercise - 1A
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  2. If 3x+(1)/(2x)=5 then what is the value of 27x^(3)+(1)/(8x^(3))?

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  3. If (a-3)^(2)+(b-4)^(2) +(c-9)^(2)=0 then what is the value of sqrt(a+b...

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  4. If average of x and (1)/(x) (x ne 0) is M then what is the average ...

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  5. If a,b, c are real and a^(2) + b ^(2) + c ^(2) = 2 (a - b - c) -3, the...

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  6. If a + b + c =0 then the value of (1)/((a + b ) (b + c)) + (1)/( (b ...

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  7. If 5x^(2) -4xy +y^(2) -2x +1=0 then value of x+y is

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  8. If x= b + c - 2a , y = c + a - 2 b , z = a + b -2 c then the value o...

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  9. (y-z)^3 + (z-x)^3 + (x-y)^3 is equal to:

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  10. If x = 2 - 2 ^(1 // 3) + 2^(2//3) , then the value of x^(3) - 6 x ...

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  11. If a^(3) - b ^(3) - c^(3) - 3abc = 0 then

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  12. If x ^(2) - 3 x + 1 =0, then what is the value of x ^(3) + (1)/(x ^(3...

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  13. If 2x + (1)/(3x) = 5, the value of (5x )/( 6x ^(2) + 20 x + 1 ) is

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  14. If m + (1)/( m - 2) = 4 find the value of (m - 2) ^(2) (1)/( ( m - 2)^...

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  15. If a ^(2)= b + c, b ^(2) = a + c, c ^(2) = b +a , then what will be t...

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  16. IF (a )/( 1 - a) + (b)/( 1 - b) + (c)/(1 - c) = 1 then the value of ...

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  17. If a^(2) + b^(2) + 2b + 4a + 5 = 0 , then the value of (a - b)/( a + ...

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  18. If (x)/(( b - c) ( b + c - 2a)) = (y)/(( c - a)( c + a- 2 b)) = (z)/(...

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  19. If (x^(3) +3x)/(3x^(2)+1)=(189)/(61) then value of x is

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  20. If (x^(2)+y^(2)) (p^(2) +q^(2)) =(xp +yq)^(2) then

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