Question

Rezolvați in R ecuația :
a.(x-)(x+4)-2(3x-2)=(x-4)*;
b.(x+5)(x+2)-3(4x-3)=(x-5)*;
c.x(x+2)-13=(x-3)(x+3);
d.4x(x-1)=(2x+5)(2x-5)+1.

Answer 1

a)
-x - 4 + 2•3x + 4 + x = (x - 4)
-6x = (x - 4)
6x = -x + 4
- (-6x) • (-1) = (x-4) • (-1)
6x + x = -x + x + 4
7x = 4
x = 4 / 7
S = { 4/7}

b)
x² + x•2 + 5x + 10 + -3•4x + 9 = (x-5)
x² - 12x + 2x + 5x + 19 = (x-5)
x² - 5x + 19 = (x-5)
x² - 5x + 19 = x-5
x² - 6x + 24 = 0
x² - 5x + 19 + -x + 5 = x-5 + -x + 5
x = 6±√(-6)² - 4•1•24 / 2•1
x = 6±√36 - 96 / 2
S = {6±√36 - 96 / 2}

c)
x² + x•2 - 13 = x² + x•3 - 3x - 9
x² + 2x - 13 = x² + 3x - 3x - 9
x² + 2x - 13 = x² - 9
x² + 2x = x² + 4
x² + 2x - 13 + 13 = x² - 9 + 13
x² + 2x - x² = x² - x² + 4
x² + 2x - 13 = x² - 9
x = 2
S = {2}

d)
4xx - 4x • 1 = (2x)² - 2x • 5 + 5•2x - 25 + 1
4x² - 4x = 2²x² - 10x + 10x - 24
4x² - 4x = 4x² - 24
4x² - 4x - 4x² = 4x² - 4x² - 24
-4x = -24
x = -24
S = {-24}.

Answer 2

b)
x² + 2 x+ 5x + 10 -12x + 9 = (x-5)
x² - 12x + 2x + 5x + 19 = x-5
x² - 5x + 19 -x+5=0
x² - 6x + 24 = 0
Δ=b²-4ac=36-4×24=36-96= - 60  ∠ 0   ⇒   ecuatia nu are solutii reale

c)
x² + 2x - 13 = x² - 9
x² + 2x - 13-x²+9=0
2x-4=0
2x = 4   ⇒  x=4/2   ⇒   x=2
S = {2}

d) 4x² - 4x = 4x² - 25+1
4x² - 4x - 4x² + 24 =0
-4x = -24 x = -24/-4    ⇒   x=6
S = {6}.