
Any expression f(a,b) involving two numbers a and b is said to be symmetric if it remains unchanged when a and b are interchanged [i.e f(a,b) = f(b,a)]. Some of the symetric functions of a and b are a^{2}+b^{2}, a^{3}+b^{3}, ab, a^{2}b^{2}+ab, 1/a+1/b, 1/a^{2} + 1/b^{2} The expression f(a,b) = a^{2}b is not symmetric because f(b,a) = b^{2}a not equal to a^{2}b = f(a,b) All symmetric functions of a and b can be expressed in terms of two symmetric functions a+b and ab. For instance, a^{3} + b^{3} = (a+b)^{3}3ab(a+b) 1/a + 1/b = (a+b)/ab 1/a^{2}+1/b^{2} = [(a+b)^{2}2ab]/(ab)^{2} a^{2}b+ab^{2} = ab(a+b) We thus observe, without actually solving the quadratic equation ax^{2}+bx+c = 0, a not equal to 0, that
Example: If a, b are the roots of the equation 2x^{2}+3x+7 = 0, then find a^{2}+b^{2}
Directions: Solve the following 