Question

URGENTEEEE!!!!! ME AJUDEM PF ME EXPLIQUE COMO FAZ VAI CAIR NA PROVA E NAO INTENDI
Determine(COM AS CONTAS) o conjunto solução de cada equação
a) x² - 12x = 0
b) x² - 16 = 0
c) x² - 64 = 0
d)4 x² + 28x = 0
e) (x + x).(x - 6) = 51 - x
f) (x - 4)² + 5x (x - 1) = 16

Answer 1

a) x² - 12x = 0
x² -12x +0
Δ= b²-4ac
Δ= (-12)² -4.1.0
Δ= 144

x= -b +/- √Δ / 2a
x= -(-12) +/- √144 / 2.1
x'= 12 + 12 / 2
x'= 24/2
x'= 12

x''= 12 -12/ 2
x''= 0/2
x''= 0

S= {12,0}
 
b) x² - 16 = 0
x² = 16
x= √16
x= +/- 4

S= {4,-4}

c) x² - 64 = 0
x²= 64
x= √64
x= +/- 8

S= {8,-8}

d)4x² + 28x = 0
4x² +28x +0
Δ= b²-4ac
Δ= 28² -4.4.0
Δ= 784

x= -b +/- √Δ / 2a
x= -28 +/- √784 / 2.4
x'= -28 + 28 / 8
x'= 0/ 8
x'= 0

x''= -28 - 28 / 8
x''= -56 / 8
x''= -7

S= {0, -7 }

e) (x + x).(x - 6) = 51 - x
x² -6x +x² -6x = 51 -x
x² +x² -6x -6x +x = 51
2x² -12x +x = 51
2x² -11x -51
Δ= b²-4ac
Δ= (-11)² -4.2.(-51)
Δ= 121 + 408
Δ= 529

x= -b +/- √Δ / 2a
x= -(-11) +/- √559 / 2.2
x'= 11 +23 / 4
x'= 34/ 4 (simplificando por 2).
x'= 17 / 2

f) (x - 4)² + 5x (x - 1) = 16
( x² -2.x.(-4) + (-4)² ) + 5x² -5 = 16
( x² +8x +16 ) +5x² -5 = 16
x² +5x² +8x = 16 -16 +5
6x² +8x = 5
6x² +8x -5
Δ= b²-4ac
Δ= 8² -4.6.(-5)
Δ= 64 + 120
Δ= 184


x= -b +/- √Δ / 2a
x= -8 +/- √184 / 2.6
x'= -8 +  3,6 / 12
x'= -4,4 / 12 

x''= -8 - 3,6 / 12
x''= -11,6 / 12

S= { -4,4/12 ; -11,6/ 12 }

Bons estudos!

Answer 2

$a) x^{2} - 12x = 0 \to \\\\ x(x-12)=0\\\\ x=0\\\\ x-12=0\to x=12\\\\\\ S=(0;12)$





$b) x^2 - 16 = 0\to \\\\ x^{2} =16\to \\\\ x=\pm \sqrt{16} \to\\\\ x=\pm4\\\\\\ S=(-4;4)$





$c) x^{2} - 64 = 0\to \\\\ x^{2} =64\to \\\\ x=\pm \sqrt{64} \to x=\pm8\\\\\\ S=(-8;8)$





$d)4 x^{2} + 28x = 0\to \\\\ x(4x+28)=0\\\\ x=0\\\\ 4x+28=0\to 4x=-28\to x= \frac{-28}{4} \to x=-7\\\\\\ S=(-7;0)$





$e) (x + x).(x - 6) = 51 - x\\\\ x^{2} -6x+ x^{2} -6x=51-x\to \\ x^{2} -6x+ x^{2} -6x-51+x=0\to \\ 2 x^{2} -11x-51=0\\a=2;b=-11;c=-51\\ \Delta=b^2-4ac\to \Delta=(-11)-4*2*(-51)\to \Delta=121+408\to \\ \Delta=529 \\\\ x' \neq x''\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-11)\pm \sqrt{529} }{2*2} \to x= \frac{11\pm 23 }{4} \to \\\\x'= \frac{11+23 }{4} \to x'= \frac{34 }{4} \to \to x= \frac{17 }{2}\\\\ x''= \frac{11- 23 }{4} \to x''= \frac{-12 }{4} \to x''=-3\\\\\\ S=(-3; \frac{17 }{2})$





$f) (x - 4)^2 + 5x (x - 1) = 16\to \\\\ x^{2} -4x-4x+16+5 x^{2} -5x-16=0\to \\\\ 6 x^{2} -13x=0 \\\\\\ x(6x-13)=0\\\\ x=0\\\\ 6x-13=0\to 6x=13\to x= \frac{13}{6} \\\\\\ S=(0;\frac{13}{6} )$