Question

Resolva as equações a seguir

Answer 1

a)3x^2+15x=0
x(3x+15)=0. 3x+15=0
x=0. 3x=-15
x=-15/3
x= -5

b)2y^2-y/3=0
6y^2-y/3=0
2y^2-y=0
y(2y-1)=0
y=0. 2y-1=0
2y=1
1/2


c)9(2n-5).(n+2)
(18n-40).(n+2)
18n^2+36n- 40n-80
18n^2-4n-80
a=18 b= -4 c= -80
x= -b+- RAIZ QUADRADA b^2-4ac/2a
x=-(-4)+- RAIZ QUADRADA (-4)^2-4.18.(-80)/2.18
x=4+- RAIZ QUADRADA 16+5760/36
x=4+-RAIZ QUADRADA 5776/36
x=4+-76/36
x1=4+76/36
x1=80/36
x1=2,22

x2=4-76/36
x2=-72/36
x2= -2

d)2x-3/x-6=3x-1/x-2
(2x-3).(x-2)=(x-6).(3x-1)
2x^2-4x-3x+6=3x^2-x-18x+6
2x^2-7x+6=3x^2-19x+6
2x^2-3x^2-7x+19x+6-6=0
-x^2+12x=0 (-1)
x^2-12x=0
x(x-12)=0
x1=0. x-12=0
x2=12

a)5x^2+12x=0
5x(x+12)=0
5x=0. x+12=0
x=0/5. x2= -12
x1=0

Answer 2

Explicação passo-a-passo:

a)

$\bf{ {3x}^{2} + 15x = 0 }$

$\bf{x = \frac{ - 15\pm \sqrt{ {15}^{2} - 4 \times 3 \times 0 } }{2 \times 3} }$

$\bf{x = \frac{ - 15\pm \sqrt{ {15}^{2} - 0} }{2 \times 3} }$

$\bf{x = \frac{ - 15\pm \sqrt{ {15}^{2} - 0} }{6} }$

$\bf{x = \frac{ - 15\pm \sqrt{ {15}^{2} } }{6} }$

$\bf{x = \frac{ - 15\pm15}{6} }$

$\bf{x = \frac{ - 15 + 15}{6} } \\ \bf{x = \frac{ - 15 - 15}{6} }$

$\bf{x = 0} \\ \bf{x = - 5}$

$\boxed{ \bf{ x_{1} = 0 }} \\ \boxed{ \bf{ x_{2} = - 5}}$

b)

$\bf{ {2y}^{2} - \frac{y}{3} = 0 }$

$\bf{3( {2y}^{2} - \frac{y}{3} ) = 3 \times 0}$

$\bf{3 \times {2y}^{2} - 3 \times \frac{y}{3} = 0 }$

$\bf{ {6y}^{2} - \cancel{3} \times \frac{y}{\cancel{3}} = 0 }$

$\bf{ {6y}^{2} - y = 0 }$

$\bf{y = \frac{ - ( - 1)\pm \sqrt{ {( - 1)}^{2} - 4 \times 6 \times 0} }{2 \times 6} }$

$\bf{y = \frac{1\pm \sqrt{ {( - 1)}^{2} - 4 \times 6 \times 0 } }{2 \times 6} }$

$\bf{y = \frac{1\pm \sqrt{1 - 4 \times 6 \times 0} }{2 \times 6} }$

$\bf{y = \frac{1\pm \sqrt{1 - 0} }{2 \times 6} }$

$\bf{y = \frac{1\pm \sqrt{1 - 0} }{12} }$

$\bf{y = \frac{1\pm \sqrt{1} }{12} }$

$\bf{y = \frac{1\pm1}{12} }$

$\bf{y = \frac{1 + 1}{12} } \\ \bf{y = \frac{1 - 1}{12} }$

$\bf{y = \frac{1}{6} } \\ \bf{y = 0}$

$\boxed{ \bf{ y_{1} = \frac{1}{6} }} \\ \boxed{ \bf{ y_{2} = 0 }}$

c)

$\bf{9 \times (2n - 5) \times (n + 2) = 0}$

$\bf{(18n - 45) \times (n + 2) = 0}$

$\bf{18n \times n + 18n \times 2 - 45n - 45 \times 2 = 0}$

$\bf{ {18n}^{2} + 36n - 45n - 90 = 0}$

$\bf{ {18n}^{2} - 9n - 90 = 0 }$

$\bf{( {18n}^{2} - 9n - 90) \div 9 = 0 \div 9}$

$\bf{ {2n}^{2} - n - 10 = 0}$

$\bf{n = \frac{ - ( - 1)\pm \sqrt{ {( - 1)}^{2} - 4 \times 2 \times ( - 10)} }{2 \times 2} }$

$\bf{n = \frac{1\pm \sqrt{ {( - 1)}^{2} - 4 \times 2 \times ( - 10) } }{2 \times 2} }$

$\bf{n = \frac{1\pm \sqrt{1 - 4 \times 2 \times ( - 10)} }{2 \times 2} }$

$\bf{n = \frac{1\pm \sqrt{ 1 + 80 } }{4} }$

$\bf{n = \frac{1\pm \sqrt{81} }{4} }$

$\bf{n = \frac{1\pm9}{4} }$

$\bf{n = \frac{1 + 9}{4} } \\ \bf{n = \frac{1 - 9}{4} }$

$\bf{n = \frac{5}{2} } \\ \bf{n = - 2}$

$\boxed{ \bf{ n_{1} = \frac{5}{2} }} \\ \boxed{ \bf{ n_{2} = - 2 }}$

d)

$\bf{ \frac{2x - 3}{x - 6} = \frac{3x - 1}{x - 2} }$

$\bf{(2x - 3) \times (x - 2) = (3x - 1) \times (x - 6)}$

$\bf{(2x - 3) \times (x - 2) - (3x - 1) \times (x - 6) = 0}$

$\bf{ {2x}^{2} - 4x - 3x + 6 - ( {3x}^{2} - 18x - x + 6) = 0}$

$\bf{ {2x}^{2} - 4x - 3x + 6 - ( {3x}^{2} - 19x + 6) = 0 }$

$\bf{ {2x}^{2} - 4x - 3x + 6 { - 3x}^{2} + 19x - 6 = 0 }$

$\bf{ {2x}^{2} - 4x - 3x\cancel{ + 6} - {3x}^{2} + 19x\cancel{ - 6} = 0}$

$\bf{ {2x}^{2} - 4x - 3x - {3x}^{2} + 19x = 0}$

$\bf{ { - x}^{2} - 4x - 3x + 19x = 0}$

$\bf{ - {x}^{2} + 12x = 0}$

$\bf{ - x \times (x - 12) = 0}$

$\bf{x \times (x - 12) = 0}$

$\bf{x = 0} \\ \bf{x - 12 = 0}$

$\bf{x = 0} \\ \bf{x = 12}$

$\boxed{ \bf{ x_{1} = 0 }} \\ \boxed{ \bf{ x_{2} = 12 }}$