Question

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Answer 1

№7   1)

 

$frac{x^2}{5}-frac{2x}{3}=frac{x^2-5}{6} \6x^2-20x=5x^2-25 \x^2-20x+25=0 \D=b^2-4ac=400-100=300 \x_1=frac{-b+sqrt{D}}{2a}=frac{20+sqrt{300}}{2}= frac{20+10sqrt{3}}{2} =10+5sqrt{3}\x_2=10-5sqrt{3}$

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           2)

$frac{x(x-7)}{3}-1=frac{11x}{10}-frac{x-4}{3} \10x^2-70x-30=33x-10x+40 \10x^2-93x-70=0 \D=b^2-4ac=8649+2800=11449=107^2 \x_1=frac{-b+sqrt{D}}{2a}=frac{93+107}{2*10}=10 \x_2=frac{-b+sqrt{D}}{2a}=-frac{14}{20}=- 0.7$

 

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$frac{(x+3)^2}{5}+1-frac{(3x-1)^2}{5}=frac{x(2x-3)}{2} \\2x^2+12x+18+10-18x^2+12x-2=10x^2-15x \-26x^2+39x+26=0 \2x^2-3x-2=0 \D=b^2-4ac=9+16=25 \x_1=frac{-b+sqrt{D}}{2a}=frac{3+5}{4}=2 \x_2=frac{-b-0sqrt{D}}{2a}=frac{3-5}{4}=-0.5$

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$frac{5x-0.25x^2}{3}-frac{(x-11)^2}{4}=6.25-frac{(7-x)^2}{2} \20x-x^2-3x^2+66x-363=75-294+84x-6x^2 \2x^2+2x-144=0 \x^2+x-72=0 \D=b^2-4ac=1+288=289=17^2 \x_1=frac{ -b+sqrt{D}}{2a}=frac{-1+17}{2}=8 \x_2=frac{ -b-sqrt{D}}{2a}=frac{-1-17}{2}=-9$

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$frac{2x^2}{5}-frac{4x-2}{3}=-0.2x \6x^2-20x+10=-3x \6x^2-17x+10=0 \D=b^2-4ac=289-240=49=7^2 \x_1=frac{-b+sqrt{D}}{2a}=frac{17+7}{12}=2 \x_2=frac{-b-sqrt{D}}{2a}=frac{10}{12}=frac{5}{6}$

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$frac{x^2-x}{3}-frac{4+x}{5}=0.2x \\5x^2-5x-12-3x=3x \5x^2-11x-12=0\D=b^2-4ac=121+240=361=19^2 \x_1=frac{-b+sqrt{D}}{2a}=frac{11+19}{10}=3 \x_2=frac{-b-sqrt{D}}{2a}=frac{11-19}{10}=-0.8$