Rút gọn các biểu thức sau A, 5 căn48 - 4căn27 -2 căn57 + căn108 B, 2 căn24 - 2 căn54 + 3căn6 - căn150
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\(P=\left|5-\sqrt{24}\right|+3+\sqrt{24}=5-\sqrt{24}+3+\sqrt{24}=8\)
\(P=\left|5-\sqrt{24}\right|+3+\sqrt{24}\)
TH1 : \(\left|5-\sqrt{24}\right|=5-\sqrt{24}\)
TH2 : \(\left|5-\sqrt{24}\right|=-5+\sqrt{24}\)
Với TH1 thì : \(\left|5-\sqrt{24}\right|+3+\sqrt{24}=5-\sqrt{24}+3+\sqrt{24}=8\)
Với TH2 thì : \(\left|5-\sqrt{24}\right|+3+\sqrt{24}=-5+\sqrt{24}+3+\sqrt{24}=-2+2\sqrt{24}\)
\(\sqrt{12}+\sqrt{27}-\sqrt{108}-\dfrac{1}{4}\sqrt{192}\)
\(=\sqrt{2^2.3}+\sqrt{3^2.3}-\sqrt{6^2.3}-\dfrac{1}{4}\sqrt{8^2.3}\)
\(=2\sqrt{3}+3\sqrt{3}-6\sqrt{3}-\dfrac{1}{4}.8\sqrt{3}=-3\sqrt{3}\)
a/\(\sqrt{54}=3\sqrt{6}\)
b/\(\sqrt{50a}=\sqrt{50}.\sqrt{a}=5\sqrt{2}.\sqrt{a}\)
c/ \(\sqrt{5\left(\sqrt{3}\right)^2=}\sqrt{5.3}=\sqrt{15}\)
a) \(\sqrt{54}=\sqrt{9.6}=\sqrt{9}.\sqrt{6}=3\sqrt{6}\)
b) \(\sqrt{50a}=\sqrt{25.2a}=\sqrt{5^2.2a}=5\sqrt{2a}\)
`Answer:`
`a)`
`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`
`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`
`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`
`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`
`=>A=-2x^2+28x-6`
`b)`
`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`
`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`
`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`
`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`
Thay `x=-7` vào ta được:
`B=10(-7)^2-2(-7)^3-7(-7)-6`
`=>B=10.49-2(-343)+49-6`
`=>B=490+686+49-6`
`=>B=1219`
a,M=2^0-2^1+2^2-2^3+2^4-2^5+.....+2^2012
2M=2^1-2^2+2^3-2^4+2^5-2^5+......-2^2012+2^2013
3M=2^0+2^2013
M=(2^0+2^2013)÷3
Vậy.......
b,N=3-3^2+3^3-3^4+3^5-3^6+.....+3^2011-3^2012
3N=3^2-3^3+3^4-3^5+3^6-3^7+......+3^2012-3^2013
4N=3-3^2013
N=(3-3^2013)÷4
Vậy........
K tao nhé ko lên lớp tao đánh m😈😈😈
b: \(x-2\sqrt{xy}+y=\left(\sqrt{x}-\sqrt{y}\right)^2\)
\(a,=\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=\sqrt{2}\\ b,=\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}=-\sqrt{5}\\ c,=\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}=\dfrac{\sqrt{6}}{2}\)
a) \(A=\sqrt{18}.\sqrt{2}-\sqrt{48}:\sqrt{3}=\sqrt{18.2}-\sqrt{48:3}\)
\(=\sqrt{36}-\sqrt{16}=6-4=2\)
b) \(B=\dfrac{8}{\sqrt{5}-1}+\dfrac{8}{\sqrt{5}+1}=\dfrac{8\sqrt{5}+8+8\sqrt{5}-8}{\left(\sqrt{5}-1\right).\left(\sqrt{5}+1\right)}=\dfrac{16\sqrt{5}}{4}=4\sqrt{5}\)
a: \(=20\sqrt{3}-12\sqrt{3}-2\sqrt{57}+6\sqrt{3}=14\sqrt{3}-2\sqrt{57}\)
b: \(=4\sqrt{6}-6\sqrt{6}+3\sqrt{6}-5\sqrt{6}=-4\sqrt{6}\)