Question

If a2 + b2 + c2 = 2(a + 2b – 2c) – 9 then find the value of a + b + c

(A) 2 (B) 3

(C) 1 (D) none of these​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of a + b + c is 1.

Step-by-step explanation:

The given equation is

$a^2+b^2+c^2=2(a+2b-2c)-9$

Using distributive property

$a^2+b^2+c^2=2a+2(2b)+2(-2c)-9$

$a^2+b^2+c^2=2a+4b-4c-9$

$a^2+b^2+c^2-2a-4b+4c+9=0$

$(a^2-2a+1)+(b^2-4b+4)+(c^2+4c+4)=0$

Using the properties of algebra.

$(a-1)^2+(b-2)^2+(c+2)^2=0$

The sum of squares x and y is zero if x=0 and y=0.

$a-1=0\Rightarrow a=1$

$b-2=0\Rightarrow b=2$

$c+2=0\Rightarrow c=-2$

The value of a + b + c is

$a+b+c=1+2-2=1$

Therefore, the value of a + b + c is 1.

#Learn more

(a+b+c)2=a2+b2+c2+2ab+2b+2ca---verify

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