Найдите корни уравнения .1. 6x(x+3)=2(x+23) 2....

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Найдите корни уравнения .1. 6x(x+3)=2(x+23) 2. 5y(y-4)=10(y-8) 3.7(6-2t)=21(4-t) 4.4(2z-8)=6(6+2z)


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3x(x+3)=x+23 \\\\

3x^2+9x=x+23 \\\\

3x^2+9x-x-23=0 \\\\

3x^2+8x-23=0 \\\\

D=8^2-4\cdot 3\cdot (-23)=64+276=340=2\sqrt{85} \\\\

x_{1,2} = \dfrac{-8\pm 2\sqrt{85}}{6} \\\\

x_1 = \dfrac{-8+2\sqrt{85}}{6} = \dfrac{2(-4+\sqrt{85})}{6} = \dfrac{-4+\sqrt{85}}{3} \\\\

x_2=\dfrac{-8-2\sqrt{85}}{6} = \dfrac{2(-4-\sqrt{85})}{6} = \dfrac{-4-\sqrt{85}}{3}" alt="1. \; \; 6x(x+3)=2(x+23) \; \; \; \mid \; \div 2 \\\\

3x(x+3)=x+23 \\\\

3x^2+9x=x+23 \\\\

3x^2+9x-x-23=0 \\\\

3x^2+8x-23=0 \\\\

D=8^2-4\cdot 3\cdot (-23)=64+276=340=2\sqrt{85} \\\\

x_{1,2} = \dfrac{-8\pm 2\sqrt{85}}{6} \\\\

x_1 = \dfrac{-8+2\sqrt{85}}{6} = \dfrac{2(-4+\sqrt{85})}{6} = \dfrac{-4+\sqrt{85}}{3} \\\\

x_2=\dfrac{-8-2\sqrt{85}}{6} = \dfrac{2(-4-\sqrt{85})}{6} = \dfrac{-4-\sqrt{85}}{3}" align="absmiddle" class="latex-formula">

image

6-2t=3(4-t) \\\\

6-2t=12-3t \\\\

-2t+3t=12-6 \\\\

t=6" alt="3. \; \; 7(6-2t)=21(4-t) \; \; \; \mid \; \div \; 7 \\\\

6-2t=3(4-t) \\\\

6-2t=12-3t \\\\

-2t+3t=12-6 \\\\

t=6" align="absmiddle" class="latex-formula">

image

y(y-4)=2(y-8) \\\\

y^2-4y=2y-16 \\\\

y^2-4y-2y+16=0 \\\\

y^2-6y+16=0 \\\\

D=(-6)^2-4\cdot 1\cdot 16 = 36-64 = -28<0 \; \; , \; \; net \: korney." alt="2. \; \; 5y(y-4)=10(y-8) \; \; \; \mid \; \div \; 5 \\\\</p>

y(y-4)=2(y-8) \\\\

y^2-4y=2y-16 \\\\

y^2-4y-2y+16=0 \\\\

y^2-6y+16=0 \\\\

D=(-6)^2-4\cdot 1\cdot 16 = 36-64 = -28<0 \; \; , \; \; net \: korney." align="absmiddle" class="latex-formula">

image

6-2t=3(4-t) \\\\

6-2t=12-3t \\\\

-2t+3t=12-6 \\\\

t=6" alt="4. \; \; 7(6-2t)=21(4-t) \; \; \; \mid \; \div \; 7 \\\\

6-2t=3(4-t) \\\\

6-2t=12-3t \\\\

-2t+3t=12-6 \\\\

t=6" align="absmiddle" class="latex-formula">

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