\(a.A=\left(x-2\right)^2+\left(y+1\right)^2+1\ge1\forall x;y\) . " = " \(\Leftrightarrow x=2;y=-1\) 

b.\(B=7-\left(x+3\right)^2\le7\forall x\)  " = " \(\Leftrightarrow x=-3\)

c.\(C=\left|2x-3\right|-13\ge-13\forall x\)  " = " \(\Leftrightarrow x=\dfrac{3}{2}\)

d.\(D=11-\left|2x-13\right|\le11\forall x\)  " = " \(\Leftrightarrow x=\dfrac{13}{2}\)

??

a) 9 234 : [3 . 3. (1 + 8³)] = 9 234 : [3 . 3 . (1 + 512)]

= 9 234 : [3 . 3 . 513] = 9 234 : 4617 = 2

b) 76 - {2 . [2 . 5² - (31 - 2 . 3)]} + 3 . 25

= 76 - {2 . [2 . 25 - (31 - 6)]} + 75 

= 76 - {2 . [50 - 25]} + 75 = 76 - {2 . 25} + 75 = 76 - 50 + 75 = 101

a) 9 234 : [3 . 3. (1 + 8³)] = 9 234 : [3 . 3 . (1 + 512)]

= 9 234 : [3 . 3 . 513] = 9 234 : 4617 = 2

b) 76 - {2 . [2 . 5² - (31 - 2 . 3)]} + 3 . 25

= 76 - {2 . [2 . 25 - (31 - 6)]} + 75 

= 76 - {2 . [50 - 25]} + 75 = 76 - {2 . 25} + 75 = 76 - 50 + 75 = 10

 a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

 a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

a) Ta có: \(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\cdot\sqrt{3}\)

\(=\left(7\cdot4\sqrt{3}+3\cdot3\sqrt{3}-2\cdot2\sqrt{3}\right)\cdot\sqrt{3}\)

\(=33\sqrt{3}\cdot\sqrt{3}\)

=99

b) Ta có: \(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)

\(=\left(12\cdot5\sqrt{2}-8\cdot10\sqrt{2}+7\cdot15\sqrt{2}\right):\sqrt{10}\)

\(=\dfrac{85\sqrt{2}}{\sqrt{10}}=\dfrac{85}{\sqrt{5}}=17\sqrt{5}\)

c) Ta có: \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)\cdot3\sqrt{6}\)

\(=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\cdot2\sqrt{2}\right)\cdot3\sqrt{6}\)

\(=\left(2\sqrt{6}-4\sqrt{3}+3\sqrt{2}\right)\cdot3\sqrt{6}\)

\(=36-36\sqrt{2}+18\sqrt{3}\)

d) Ta có: \(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)

\(=3\cdot\sqrt{75\sqrt{2}}+5\cdot\sqrt{48\sqrt{2}}-4\sqrt{48\sqrt{2}}\)

\(=3\cdot5\sqrt{2}\cdot\sqrt{\sqrt{2}}+4\sqrt{3}\sqrt{\sqrt{2}}\)

\(=15\sqrt{\sqrt{8}}+4\sqrt{\sqrt{18}}\)

a,=\(\left(28\sqrt{3}+9\sqrt{3}-4\sqrt{3}\right).\sqrt{3}\)

   \(=28.3+9.3-4.3=99\)

b,\(=\left(60\sqrt{2}-80\sqrt{2}+175\sqrt{2}\right):\sqrt{10}\)

  \(=155\sqrt{2}:\sqrt{10}=\dfrac{155}{\sqrt{5}}\)

d,Ta có:\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)

        \(=3\sqrt{75\sqrt{2}}+5\sqrt{48\sqrt{2}}-4\sqrt{48\sqrt{2}}\)

        \(=15\sqrt{3\sqrt{2}}+20\sqrt{3\sqrt{2}}-16\sqrt{3\sqrt{2}}\)

        \(=19\sqrt{3\sqrt{2}}\)

A = ( 1/33 - 13/55 + 17/777) . 0

A = 0

\(a,log_272-\dfrac{1}{2}\left(log_23+log_227\right)\\ =log_272-\dfrac{1}{2}log_2\left(3\cdot27\right)\\ =log_272-log_2\left(81\right)^{\dfrac{1}{2}}\\ =log_272-log_29\\ =log_2\dfrac{72}{9}\\ =log_28\\ =3\)

\(b,5^{log_240-log_25}\\ =5^{log_2\dfrac{40}{5}}\\ =5^{log_28}\\ =5^3\\ =125\)

\(c,3^{2+log_92}\\ =3^{log_9\left(81\cdot2\right)}\\ =3^{\dfrac{1}{2}log_3162}\\ =\left(162\right)^{\dfrac{1}{2}}\\ =\sqrt{162}\\ =9\sqrt{2}\)

a) 4 500 : 90 : 25 = 50 : 25 = 2

b) 840 : (3 x 4) = 840 : 12 = 70

c) 682 + 96 : 12 = 682 + 8 = 690

d) 2 784 : 24 – 16 = 116 – 16 = 100

\(a.\left(1496+3672\right):34-17\\ =5168:34-17\\ =152-17=135\\ b.8307:\left(14\times2+200\right)\\ =8307:\left(28+200\right)\\ =8307:228=\dfrac{2769}{76}\\ c.\left(328\times75\right):82+56432\\ =24600:82+56432\\ =300+56432=56732\)

a, = 5168 : 34 - 17

    = 152 - 17

    = 135

b, = 8307 : ( 28 + 200 ) 

    = 8307 : 228

    = \(\dfrac{2769}{76}\)

c, = 24600 : 82 + 56432

    = 300 + 56432

    = 56732

a) \(\left(1496+3672\right):34-17=5168:34-17=152-17=135\)

b) \(8307:\left(14x2+200\right)=8307:\left(28+200\right)=8307:228=\dfrac{8307}{228}=\dfrac{2769}{76}\)

c) \(\left(328x75\right):82+56432=24600:82+56432\)

\(=300+56432=56732\)