Find $a^2 + b^2 + c^2$ Value
We are given the following information:
- Sum of variables: $a + b + c = 10$
- Sum of products of pairs: $ab + bc + ca = 31$
We need to find the value of $a^2 + b^2 + c^2$.
Algebraic Identity Application
We use the algebraic identity:
$ (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) $
Substituting Given Values
Substitute the known values into the identity:
$ (10)^2 = a^2 + b^2 + c^2 + 2(31) $
Calculation Steps
Simplify the equation:
$ 100 = a^2 + b^2 + c^2 + 62 $
Isolate $a^2 + b^2 + c^2$:
$ a^2 + b^2 + c^2 = 100 - 62 $
$ a^2 + b^2 + c^2 = 38 $
Conclusion
The value of $a^2 + b^2 + c^2$ is 38.
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Important Questions from Identities
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