1)100x²-49y²=(10x)²-(7y)²=(10x+7y)(10x-7y)
2)36a²+12a+1=(6a)²+2.6a.1+1²=(6a+1)²
3)3x²+x=0, x(3x+1)=0
a)x=0
b)3x+1=0, x=-1/3
4)49x-x³=0, x(49-x²)=0, x(7+x)(7-x)=0
a)x=0
b)7+x=0, x=-7
c)7-x=0, x=7
1
[ctg(x+π/3)=0⇒x+π/3=π/2+πk⇒x=π/6+πk,k∈z
{cos(x/2)-1=0⇒cos(x/2)=1⇒x/2=2πk⇒x=4πk,k∈z
2
3crg(x/3)=3
ctg(x/3)=1
x/3=π/4+πk
x=3π/4+3πk,k∈z
-7π/2≤3π/4+3πk≤5π/4
-14≤3+12k≤5
-17≤12k≤2
-17/12≤k≤2/12
k=-1,0
Ответ 2 корня