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Муодиларо ҳал кунед: \((3x+5)^2+(x+6)^3=4x^2+1\)

\((3x+5)^2+(x+6)^3=4x^2+1\)

\((3x+5)^2+(x+6)^3-4x^2-1=0\)

\((3x+5)^2+(x+6)^3-(2x)^2-1^3=0\)

\(((3x+5)^2-(2x)^2)+((x+6)^3-1^3)=0\)

\((3x+5)^2-(2x)^2=(3x+5+2x)(3x+5-2x)=\)

\(=(5x+5)(x+5)\)

\((x+6)^3-1^3=(x+6-1)((x+6)^2+(x+6)/cdot1+1^2)=\)

\(=(x+5)(x^2+12x+36+x+6+1)=\)

\(=(x+5)(x^2+13x+43)\)

\((5x+5)(x+5)+(x+5)(x^2+13x+43)=0\)

\((x+5)(5x+5+x^2+13x+43)=0\)

\((x+5)(x^2+18x+48)=0\)

\(x+5=0\)

\(x_1=-5\)

\(x^2+18x+48=0\)

\(D=324-4\cdot48=\)

\(=324-192=132\)

\(x_2=\frac{-18-\sqrt{132}}{2}=\)

\(=\frac{-18-\sqrt{4\cdot33}}{2}=\)

\(=\frac{-18-2\cdot\sqrt{33}}{2}=\)

\(=\frac{2\cdot(-9-\sqrt{33})}{2}=\)

\(=-9-\sqrt{33}\)

\(x_3=\frac{-18+\sqrt{132}}{2}=\)

\(=\frac{-18+\sqrt{4\cdot33}}{2}=\)

\(=\frac{-18+2\cdot\sqrt{33}}{2}=\)

\(=\frac{2\cdot(-9+\sqrt{33})}{2}=\)

\(=-9+\sqrt{33}\)

Ҷавоб: \(x_1=-5\); \(x_2=-9-\sqrt{33}\); \(x_3=-9+\sqrt{33}\).