Question

X^3 + (p+3)x^2 - 2(2p+1)x + 5 = 0 jika x1^2 + x2^2 + x3^2 minimum, berapa nilai p?

Answer 1

X1^2 + x2^2 + x3^2 harus minimum
karena semua bilangan yg dikuadratkan pasti positif, maka x1^2 + x2^2 + x3^2 = 0

x1^2 + x2^2 + x3^2 = (x1 + x2 + x3)^2 - 2(x1x2 + x2x3 +x1x3)
x1^2 + x2^2 + x3^2 = (-b/a)^2 - 2(c/a)
0 = p^2 + 6p + 9 + 8p + 4
0 = p^2 + 14p + 13
0 = (p + 1)(p + 13)
p = -1 atau p = -13

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