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.
Similar Questions
If $a + b + c = 0$, then find the value of $\frac{(a^2+b^2+c^2)^2}{a^2b^2+b^2c^2+c^2a^2}$
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Important Questions from Identities
If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of \(27x^3+{{1} \over 8x^3}\) ?
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(0.73)^3+(0.31)^3}{(0.73)^2-0.73\times0.31+(0.31)^2}\)
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
