Rút gọn bt
G= a-3 sqrt a sqrt a -3 - (a + 4sqrt(a) + 3)/(sqrt(a) + 3) (với a>=9)
H = (9 - x)/(sqrt(x) + 3) - (9 - 6sqrt(x) + x)/(sqrt(x) - 3) -6 (với x>=9)
I = ((2sqrt(x))/(x * sqrt(x) + x + sqrt(x) + 1) - 1/(sqrt(x) + 1)) =( 2 sqrt x sqrt x +1 -1) (vớii x>=0,x #1)
J = sqrt(x + 12 + 6sqrt(x + 3)) - sqrt(x + 12 - 6sqrt(x + 3)) (với x >= 6)
k = sqrt(m ^ 2 + 6m + 9) + sqrt(m ^ 2 - 6m + 9) (Với bất kì m)
L = sqrt(a + 2sqrt(a - 1)) + sqrt(a - 2sqrt(a - 1)) (với 1 <= a <= 2)
x>=6
=>\(x+3>=9\)
=>\(\sqrt{x+3}>=3\)
=>\(\sqrt{x+3}-3>=0\)
\(J=\sqrt{x+12+6\sqrt{x+3}}-\sqrt{x+12-6\sqrt{x+3}}\)
\(=\sqrt{x+3+2\cdot\sqrt{x+3}\cdot3+9}-\sqrt{x+3-2\cdot\sqrt{x+3}\cdot3+3^2}\)
\(=\sqrt{\left(\sqrt{x+3}+3\right)^2}-\sqrt{\left(\sqrt{x+3}-3\right)^2}\)
\(=\sqrt{x+3}+3-\left(\sqrt{x+3}-3\right)=6\)
\(K=\sqrt{m^2+6m+9}+\sqrt{m^2-6m+9}\)
\(=\sqrt{\left(m+3\right)^2}+\sqrt{\left(m-3\right)^2}\)
\(=\left|m+3\right|+\left|m-3\right|\)
TH1: m<=-3
=>K=-m-3+3-m=-2m
TH2: -3<=m<=3
=>K=m+3+3-m=6
TH3: m>=3
=>K=m+3+m-3=2m
1<=a<=2
=>\(0< =a-1< =1\)
=>\(\sqrt{a-1}< =1\)
=>\(\sqrt{a-1}-1< =0\)
\(L=\sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}\)
\(=\sqrt{a-1+2\sqrt{a-1}+1}+\sqrt{a-1-2\sqrt{a-1}+1}\)
\(=\sqrt{\left(\sqrt{a-1}+1\right)^2}+\sqrt{\left(\sqrt{a-1}-1\right)^2}\)
\(=\sqrt{a-1}+1+1-\sqrt{a-1}=2\)
