Question

Resolva as equações em R:
 
3x²-1/64=2x²  

7y²-y=0 

(x+2)²=x²+(x+1)²

Answer 1

a)
$3x^2-\frac{1}{64}=2x^2 \\ \\ x^2=\frac{1}{64}\\ \\ x=\pm \frac{1}{8}$

b)
$7y^2-y=0\\ y(7y-1)=0\\ \\ y_1=0\\ \\ y_2=\frac{1}{7}$

c)
$(x+2)^2=x^2+(x+1)^2\\ \\ x^2+4x+4=x^2+x^2+2x+1\\ \\ x^2-2x-3=0\\ \\ S=\{-1,3\}\\ \\ S=2 \ \ P=3$

Answer 2

3x²-1/64=2x²
3x²-2x²=1/64
x²=1/64
x=√1/64
x=+-1/8

7y²-y=0
Δ = b² -4ac
Δ = (-1)² -4 *7 * 0
Δ= 1 -0
Δ = 1
x' = (-b + √∆)/ 2a
(-(-1) + 1)/2 * 7
(1 + 1)/14
2/14
x'' = (-b - √∆)/ 2a
(-(-1) - 1)/2 * 7
(1 - 1)/14
0/14
0

(x+2)²=x²+(x+1)²
x²+2.x.2+2²=x²+x²+2.x.1+1²
x²+4x+4=x²+x²+2x+1
x²-2x²+4x-2x=1-4
-x²+2x=-3
-x²+2x+3=0
Δ = b² -4ac
Δ = 2² -4 *(-1) * 3
Δ = 4 + 12
Δ = 16
x' = (-b + √∆)/ 2a
(-2 + 4)/2 * (-1)
(-2 + 4)/-2
2/-2
-1
x'' = (-b - √∆)/ 2a
(-2 - 4)/2 * (-1)
(-2 - 4)/-2
-6/-2
3