Question

tim gia tri nho nhat (a+1)(a+3)(a+5)(a+7)+15

Answer 1

GTNN 15

Answer 2

(a + 1)(a + 3)(a + 5)(a + 7)+15 = (a + 1)(a + 7)(a + 5)(a + 3)+15 = (a² + 8a +7)(a² + 8a +15) + 15 

Đặt a² + 8a + 11 = x => (a² + 8a +7)(a² + 8a +15) + 15  = (x-4)(x+4) +15 = x² - 4 + 15 = x² +11 \(\ge\)11

GTNN (a + 1)(a + 3)(a + 5)(a + 7) + 15 = 11 \(\Leftrightarrow\)x =0 \(\Leftrightarrow\)a² + 8a + 11 = 0 \(\Leftrightarrow\)(a + 4)² -5 = 0 \(\Leftrightarrow\)(a + 4 +\(\sqrt{5}\))(a + 4 -\(\sqrt{5}\))=0 \(\Leftrightarrow\)a = -4+ \(\sqrt{5}\)hoặc a = -4 - \(\sqrt{5}\)