+130477
ab + 6b = 32 → b(a + 6) = 32 → b = 32/(a + 6) (2)
Substitue (2) into (1) and we have
a^2 + [32/(a + 6)]^2 = 20 simplify
a^2(a + 6)^2 + 1024 = 20(a+6)^2
a^2(a^2 + 12a + 36) + 1024 = 20a^2 + 240a + 720
a^4 + 12a^3 + 36a^2 + 1024 = 20a^2 + 240a + 720
a^4 + 12a^3 + 16a^2 - 240a + 304 = 0
Using the on site solver we have one real soution for a
a4+12×a3+16×a2−240×a+304=0⇒{a=−2×√3×i−8a=2×√3×i−8a=2}⇒{a=−8−3.4641016151377546ia=−8+3.4641016151377546ia=2}
And b =
32 /(a + 6) = 32 /(2 + 6) = 32 /8 = 4
+130477
ab + 6b = 32 → b(a + 6) = 32 → b = 32/(a + 6) (2)
Substitue (2) into (1) and we have
a^2 + [32/(a + 6)]^2 = 20 simplify
a^2(a + 6)^2 + 1024 = 20(a+6)^2
a^2(a^2 + 12a + 36) + 1024 = 20a^2 + 240a + 720
a^4 + 12a^3 + 36a^2 + 1024 = 20a^2 + 240a + 720
a^4 + 12a^3 + 16a^2 - 240a + 304 = 0
Using the on site solver we have one real soution for a
a4+12×a3+16×a2−240×a+304=0⇒{a=−2×√3×i−8a=2×√3×i−8a=2}⇒{a=−8−3.4641016151377546ia=−8+3.4641016151377546ia=2}
And b =
32 /(a + 6) = 32 /(2 + 6) = 32 /8 = 4
