x + y = a ----------> x^2 + 2xy + y^2 = a^2 -----> x^2 + y^2 = a^2 - 2xy
xy = a^2 - 7a + 14 ------> 2xy = 2a^2 - 14a + 28
=>
x^2 + y^2 = a^2 - (2a^2 - 14a + 28)
x^2 + y^2 = - (a^2 - 14a + 28)
x^2 + y^2 = - (a^2 - 2*7a + 7^2 - 21)
x^2 + y^2 = - (a - 7)^2 + 21 = 21 - (a - 7)^2
(a - 7)^2 ---> 0 -----> a = 7
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x + y = a ----------> x^2 + 2xy + y^2 = a^2 -----> x^2 + y^2 = a^2 - 2xy
xy = a^2 - 7a + 14 ------> 2xy = 2a^2 - 14a + 28
=>
x^2 + y^2 = a^2 - (2a^2 - 14a + 28)
x^2 + y^2 = - (a^2 - 14a + 28)
x^2 + y^2 = - (a^2 - 2*7a + 7^2 - 21)
x^2 + y^2 = - (a - 7)^2 + 21 = 21 - (a - 7)^2
(a - 7)^2 ---> 0 -----> a = 7