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\(25\sqrt{\dfrac{x-3}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\left(x\ge3\right)\)
\(=25\sqrt{\dfrac{1}{25}.\left(x-3\right)}-7\sqrt{\dfrac{4}{9}.\left(x-3\right)}-7\sqrt{x^2-9}+18\sqrt{\dfrac{1}{9}.\left(x^2-9\right)}=0\)
\(=5\sqrt{x-3}-\dfrac{14}{3}\sqrt{x-3}-7\sqrt{x^2-9}+6\sqrt{x^2-9}=0\)
\(\Rightarrow\dfrac{1}{3}\sqrt{x-3}-\sqrt{\left(x-3\right)\left(x+3\right)}=0\Rightarrow\sqrt{x-3}-3\sqrt{\left(x-3\right)\left(x+3\right)}=0\)
\(\Rightarrow\sqrt{x-3}\left(1-3\sqrt{x+3}\right)=0\Rightarrow\left[{}\begin{matrix}\sqrt{x-3}=0\\1=3\sqrt{x+3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{26}{9}\left(l\right)\end{matrix}\right.\)
a, 410. 230=220.230=250
b,925.274.813= 350.312.312=374
Tương tự các câu khác....
a, 410.230 = (22)10.230 = 220.230 = 250
b, 925.274.813 = (32)25.(33)4.(34)3 = 350.312.312 = 374
c, 2550.1255 = (52)50.(53)5 = 5100.515 = 5115
d, 643.48.164 = (26)3.(22)8.(24)4 = 218.216.216 = 250
e, 38 : 36 = 32
210 : 83 = 210 : (23)3 = 210 : 29 = 2
127 : 67 = (12 : 6)7 = 27
@Dương Tuyết Mai
1) \(x^2+6x+9\)
\(=\left(x+3\right)^2\)
2) \(10x-25-x^2\)
\(=-25+10x-x^2\)
\(=-\left(5-x\right)^2\)
3) \(8x^3-\dfrac{1}{8}\)
\(=\left(2x\right)^3-\left(\dfrac{1}{2}\right)^3\)
\(=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
4) \(\dfrac{1}{25}x^2-64y^2\)
\(=\left(\dfrac{1}{5}x\right)^2-\left(8y\right)^2\)
\(=\left(\dfrac{1}{5}x+8y\right)\left(\dfrac{1}{5}x-8y\right)\)
\(x^2+6x+9=\left(x+3\right)^2\)
\(10x-25-x^2=-\left(x-5\right)^2\)
\(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)
b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)
c: \(16\cdot81=36^2\)
d: \(25^4\cdot2^8=100^4\)
a) x2+20x+100=x2+2.10.x+102
=(x+10)2
Tại x=-100 => ...........
(bn thay vào rồi tự tính nhá)
b) 16y2-8y+1=(4y)2-2.4y+12
=(4y-1)2
Với y=\(\frac{81}{4}\)=> ............
(bn thay vào rồi tự tính nhá)
c)x3+ 15x2+ 75x+125 =x3+3.x2.5+3.x.52+53
=(x+5)3
Với x=-25 =>....
d)x3-9x2+27x-27(đề sai đáng ra là -9x2 chứ ko phải -9x nha bn)
=x3-3.x2+3.x.32-33
=(x-3)3
Với x=13=> ....
tk mk nha
\(x^2+20x+100\)
\(=x^2+2.x.10+10^2\)
\(=\left(x+10\right)^2\)
\(=\left(-110+10\right)^2\)
\(=\left(-100\right)^2=100^2=10000\)
b) 25.(37+5) -63.(-25)+5.(-125)
= 25.42+63.25+5.25.(-5)
= 25.[42+25+5.(-5)]
= 25.[42+25-25]
= 25.42
=1050
c) 31 . (-18)+ 31.(-81)-31
= 31.(-18)+31.(-81)+31.(-1)
= 31.[-18+(-81)+(-1)]
= 31.(-100)
= -3100
a, 32684 + 41325 + 316 + 675
= (32684 + 316) + (41325 + 675)
= 33 000 + 42 000
= 75 000
b, 25 \(\times\) 18 \(\times\) 4 \(\times\) 2
= (25 \(\times\) 4) \(\times\) (18 \(\times\) 2)
= 100 \(\times\) 36
= 3600
\(\sqrt{2-x}-3\sqrt{25\left(2-x\right)}+\sqrt{81\left(2-x\right)}\)Với x =< 2
\(=\sqrt{2-x}-15\sqrt{2-x}+9\sqrt{2-x}=-5\sqrt{2-x}\)