Tính giá trị của biểu thức:
a) 82 + 13 – 76
b) 547 – 264 – 200
c) 2 × 3 × 5
d) 16 : 2 : 2
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\(a.A=\left(x-2\right)^2+\left(y+1\right)^2+1\ge1\forall x;y\) . " = " \(\Leftrightarrow x=2;y=-1\)
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) 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,\(=\left(60\sqrt{2}-80\sqrt{2}+175\sqrt{2}\right):\sqrt{10}\)
\(=155\sqrt{2}:\sqrt{10}=\dfrac{155}{\sqrt{5}}\)
\(a,log_272-\dfrac{1}{2}\left(log_23+log_227\right)\\ =log_272-\dfrac{1}{2}log_2\left(3\cdot27\right)\\ =log_272-log_2\left(81\right)^{\dfrac{1}{2}}\\ =log_272-log_29\\ =log_2\dfrac{72}{9}\\ =log_28\\ =3\)
\(b,5^{log_240-log_25}\\ =5^{log_2\dfrac{40}{5}}\\ =5^{log_28}\\ =5^3\\ =125\)
\(c,3^{2+log_92}\\ =3^{log_9\left(81\cdot2\right)}\\ =3^{\dfrac{1}{2}log_3162}\\ =\left(162\right)^{\dfrac{1}{2}}\\ =\sqrt{162}\\ =9\sqrt{2}\)
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)
82 + 13 - 76
= 95 – 76
= 19
b)
547 – 264 – 200
= 283 – 200
= 83
c)
2 × 3 × 5
= 6 × 5
= 30
d)
16 : 2 : 2
= 8 : 2
= 4