Question

If a+b+c=7 andab+bc+ac= 20 find the value of a^2+b^2+c^2

Answer 1

Answer:

9

Step-by-step explanation:

We know,

  ( a + b + c )^2 = a^2 + b^2 + c^2 + 2( ab + bc + ca )

Here,

   Squaring on both sides of a + b + c = 7 :

⇒ ( a + b + c )^2 = 7^2

⇒ a^2 + b^2 + c^2 + 2( ab + bc + ca ) = 49

    Substituting the given values:

⇒ a^2 + b^2 + c^2 + 2( 20 ) = 49

⇒ a^2 + b^2 + c^2 + 40 = 49

⇒ a^2 + b^2 + c^2 = 49 - 40 = 9

      Hence the require value of a^2 + b^2 + c^2 is 9

Answer 2

Answer:

9

Step-by-step explanation:

(a+ b+ c)^2 = a2 + b2 + c2 + 2ab + 2bc + 2bc

7^2 = a2 + b2 + c2 + 2 ( ab + bc + ca )

49 = a2 + b2 + c2 + 2× 20

49 = a2+ b2 + c2 + 40

therefore, a2 + b2 + c2 = 49 - 40 = 9

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