Δ = ∣ x 0 2 x − 3 x 4 x 6 x − x − 2 x 3 x ∣ = x ( 12 x 2 + 12 x 2 ) − 0 + 2 x ( 6 x 2 + 4 x 2 ) = 24 x 3 + 20 x 3 = 44 x 3 Δ 1 = ∣ 6 0 2 x 30 4 x 6 x 8 − 2 x 3 x ∣ = 6 ( 12 x 2 + 12 x 2 ) − 0 + 2 x ( − 60 x − 32 x ) = 144 x 2 − 184 x = 4 x ( 36 x − 46 ) Δ 2 = ∣ x 6 2 x − 3 x 30 6 x − x 8 3 x ∣ = x ( 90 x − 48 x ) − 6 ( − 9 x 2 + 6 x 2 ) + 2 x ( − 24 x + 30 x ) = 42 x + 18 x 2 + 12 x 2 = 42 x + 30 x 2 = 2 x ( 21 + 15 x ) Δ 3 = ∣ x 0 6 − 3 x 4 x 30 − x − 2 x 8 ∣ = x ( 32 x + 60 x ) − 0 + 6 ( 6 x 2 + 4 x 2 ) = 92 x 2 + 60 x 2 = 152 x 2 \begin{gathered}
\Delta=\left|\begin{array}{ccc}
x & 0 & 2 x \\
-3 x & 4 x & 6 x \\
-x & -2 x & 3 x
\end{array}\right|=x\left(12 x^{2}+12 x^{2}\right)-0+2 x\left(6 x^{2}+4 x^{2}\right) \\
=24 x^{3}+20 x^{3}=44 x^{3} \\
\Delta_{1}=\left|\begin{array}{ccc}
6 & 0 & 2 x \\
30 & 4 x & 6 x \\
8 & -2 x & 3 x
\end{array}\right|=6\left(12 x^{2}+12 x^{2}\right)-0+2 x(-60 x-32 x) \\
=144 x^{2}-184 x=4 x(36 x-46)
\\\Delta_{2}=\left|\begin{array}{ccc}
x & 6 & 2 x \\
-3 x & 30 & 6 x \\
-x & 8 & 3 x
\end{array}\right| \\
=x(90 x-48 x)-6\left(-9 x^{2}+6 x^{2}\right)+2 x(-24 x+30 x) \\
=42 x+18 x^{2}+12 x^{2}=42 x+30 x^{2}=2 x(21+15 x) \\
\Delta_{3}=\left|\begin{array}{ccc}
x & 0 & 6 \\
-3 x & 4 x & 30 \\
-x & -2 x & 8
\end{array}\right|=x(32 x+60 x)-0+6\left(6 x^{2}+4 x^{2}\right) \\
=92 x^{2}+60 x^{2}=152 x^{2}
\end{gathered} Δ = ∣ ∣ x − 3 x − x 0 4 x − 2 x 2 x 6 x 3 x ∣ ∣ = x ( 12 x 2 + 12 x 2 ) − 0 + 2 x ( 6 x 2 + 4 x 2 ) = 24 x 3 + 20 x 3 = 44 x 3 Δ 1 = ∣ ∣ 6 30 8 0 4 x − 2 x 2 x 6 x 3 x ∣ ∣ = 6 ( 12 x 2 + 12 x 2 ) − 0 + 2 x ( − 60 x − 32 x ) = 144 x 2 − 184 x = 4 x ( 36 x − 46 ) Δ 2 = ∣ ∣ x − 3 x − x 6 30 8 2 x 6 x 3 x ∣ ∣ = x ( 90 x − 48 x ) − 6 ( − 9 x 2 + 6 x 2 ) + 2 x ( − 24 x + 30 x ) = 42 x + 18 x 2 + 12 x 2 = 42 x + 30 x 2 = 2 x ( 21 + 15 x ) Δ 3 = ∣ ∣ x − 3 x − x 0 4 x − 2 x 6 30 8 ∣ ∣ = x ( 32 x + 60 x ) − 0 + 6 ( 6 x 2 + 4 x 2 ) = 92 x 2 + 60 x 2 = 152 x 2
N o w , a = Δ 1 Δ = 4 x ( 36 x − 46 ) 44 x 3 = ( 36 x − 46 ) 11 x 2 , b = Δ 2 Δ = 2 x ( 21 + 15 x ) 44 x 3 = ( 21 + 15 x ) 22 x 2 , c = Δ 3 Δ = 152 x 2 44 x 3 = 38 11 x Now, a=\frac{\Delta_{1}}{\Delta}=\frac{4 x(36 x-46)}{44 x^{3}}=\frac{(36 x-46)}{11 x^{2}},\\b=\frac{\Delta_{2}}{\Delta}=\frac{2 x(21+15 x)}{44 x^{3}}=
\frac{(21+15 x)}{22 x^{2}},\\ c=\frac{\Delta_{3}}{\Delta}=\frac{152 x^{2}}{44 x^{3}}=\frac{38}{11 x} N o w , a = Δ Δ 1 = 44 x 3 4 x ( 36 x − 46 ) = 11 x 2 ( 36 x − 46 ) , b = Δ Δ 2 = 44 x 3 2 x ( 21 + 15 x ) = 22 x 2 ( 21 + 15 x ) , c = Δ Δ 3 = 44 x 3 152 x 2 = 11 x 38
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