If a + b + c = 11 and a^2 + b^2 + c^2 = 49, what will be the value of ab + cb + ca
Answers
Answer- The above question is from the chapter 'Polynomials'.
Let's know about polynomials first.
Polynomial- It is an algebraic expression involving use of variables and constants.
p(x)- It is used to denote a polynomial. It is read is 'Polynomial in x'.
Polynomials can be classified on two basis:
1) Number of terms
E.g.- Polynomial with one term is called monomial.
Two terms- binomial
Three terms- trinomial
2) Power of variable
E.g.- Polynomial with degree 1 is called linear polynomial.
degree 2- quadratic polynomial
degree 3- cubic polynomial
degree 4- biquadratic polynomial
Concept used: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Given question: If a + b + c = 11 and a² + b² + c² = 49, what will be the value of ab + cb + ca ?
Solution: We know that (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Substituting the values, we get,
11² = 49 + 2 × (ab + bc + ca)
121 - 49 = 2 × (ab + bc + ca)
2 × (ab + bc + ca) = 72
(ab + bc + ca) = 72/2
(ab + bc + ca) = 36
∴ value of ab + cb + ca = 36.
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