Question

Gasiti multimea sulutiilor rationale ale ecuatiilor
a)3x²+7x=5(x+1)
b)2x²+10x=6(x+1)
c)3x²+13x=8(x+1)
d)2x²-5(x-1)=2
e)3x²-4(x+1)=-3x
f)(x+2)²-5x=6
g)(2x-3)²=6-5x
h)(2x+1)²+3x=-2
AJUTOR DAU 50 DE PUNCTE!!

Answer 1

a)3x²+7x=5(x+1)
3x^2+7x=5x+5
3x^2+2x−5=0
(3x+5)(x−1)=0
x=−5/3 sau x=1

b)2x²+10x=6(x+1)
2x^2+10x=6x+6
2x^2+4x−6=0
2(x−1)(x+3)=0
x=1 sau x=−3

c)3x²+13x=8(x+1)
3x^2+13x=8x+8
3x^2+5x−8=0
(3x+8)(x−1)=0
x=−8/3 sau x=1

d)2x²-5(x-1)=2
2x^2−5x+3=0
(2x−3)(x−1)=0
x=3/2 sau x=1

e)3x²-4(x+1)=-3x
3x^2−4x−4=−3x
3x^2−x−4=0
(3x−4)(x+1)=0
x=4/3 sau x=−1

f)(x+2)²-5x=6
x^2−x+4=6
x^2−x−2=0
(x+1)(x−2)=0
x=−1 sau x=2

g)(2x-3)²=6-5x
4x^2−12x+9=−5x+6
4x^2−7x+3=0
(4x−3)(x−1)=0
x=3/4 sau x=1

h)(2x+1)²+3x=-2
4x^2+7x+1=−2
4x^2+7x+3=0
(4x+3)(x+1)=0
x=−3/4 sau x=−1

Soluții raționale: −5/3, −8/3, 3/2, 4/3, 3/4, −3/4