Răspuns :
(x+7)²=x²+14x+49
(3x-2)²=9x²-12x+4
(x+6)(x-6)=x²-36
x²+12x+36=x²+2·x·6+6²=(x+6)²
25x²-10xy+y²=(5x)²-2·5x·y+y²=(5x-y)²
81x²-49y²=(9x+7y)(9x-7y)
a²x+b²-a²y-b²y=a²(x-y)+b²(1-y)
x³+4x²+4x+16=x²(x+4)+4(x+4)=(x²+4)(x+4)
x²=36
x=√36
x=6 sau -6
(x+2)²=12
x+2=√12
x+2=2√3 sau -2√3
x=2√3-2 sau -2√3-2
x=2(√3-1) sau x=-2(√3+1)
(3x-2)²=9x²-12x+4
(x+6)(x-6)=x²-36
x²+12x+36=x²+2·x·6+6²=(x+6)²
25x²-10xy+y²=(5x)²-2·5x·y+y²=(5x-y)²
81x²-49y²=(9x+7y)(9x-7y)
a²x+b²-a²y-b²y=a²(x-y)+b²(1-y)
x³+4x²+4x+16=x²(x+4)+4(x+4)=(x²+4)(x+4)
x²=36
x=√36
x=6 sau -6
(x+2)²=12
x+2=√12
x+2=2√3 sau -2√3
x=2√3-2 sau -2√3-2
x=2(√3-1) sau x=-2(√3+1)
1. (x+7)² =x²+14x+49
(3x-2)²=9x²-12x+4
(x-6)(x+6)=x²-36
2. Descompuneti:
x²+12x+36 =(x+6)²
25x²-10xy+y²=(5x-y)²
81x²-49y² =(9x-7y)(9x+7y)
x⁴+4 =(x²+2-2x)(x²+2+2x)
3.Grupati favorabil:
a²x+b²-a²y-b²y =a²x-a²y+b²-b²y =a²(x-y)-y(a²+b²)
x³+4x²+4x+16=x²(x+4)+4(x+4)=(x+4)(x²+1)
4. Rezolvati ecuatiile:
x²=36 x₁=6 x₂=-6
(x+2)²=12
solutia 1
x+2=2√3
x=2√3-2
solutia 2
x+2=-2√3
x=-2√3-2
(3x-2)²=9x²-12x+4
(x-6)(x+6)=x²-36
2. Descompuneti:
x²+12x+36 =(x+6)²
25x²-10xy+y²=(5x-y)²
81x²-49y² =(9x-7y)(9x+7y)
x⁴+4 =(x²+2-2x)(x²+2+2x)
3.Grupati favorabil:
a²x+b²-a²y-b²y =a²x-a²y+b²-b²y =a²(x-y)-y(a²+b²)
x³+4x²+4x+16=x²(x+4)+4(x+4)=(x+4)(x²+1)
4. Rezolvati ecuatiile:
x²=36 x₁=6 x₂=-6
(x+2)²=12
solutia 1
x+2=2√3
x=2√3-2
solutia 2
x+2=-2√3
x=-2√3-2