Rút gọn:a)5100-10/8160-16 ; b)952+8/2142+18
Những câu hỏi liên quan
Rút gọn:
a) A=(4-x)(16+4x+x2)-(4-x)3
b) B=(3x+2)(9x2-6x+4)-(9x2+6x+4)(3x-2)
c) C=(x+1)(x2-x+1)-x(x+1)2
a) Ta có: \(A=\left(4-x\right)\left(16+4x+x^2\right)-\left(4-x\right)^3\)
\(=64-x^3+\left(x-4\right)^3\)
\(=64-x^3+x^3-12x^2+48x-64\)
\(=-12x^2+48x\)
b) Ta có: \(B=\left(3x+2\right)\left(9x^2-6x+4\right)-\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(=27x^3+8-27x^3+8\)
=16
c) Ta có: \(C=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)^2\)
\(=x^3+1-x\left(x^2+2x+1\right)\)
\(=x^3+1-x^3-2x^2-x\)
\(=-2x^2-x+1\)
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Mọi người ơi giúp mik với!Cám ơn!
Rút gọn:A=1+2+2^2+2^3+2^4+....+2^10
2A=2+22+23+24+...+211
2A—A=(2+22+23+24+....+211)—(1+2+22+23+...+210)
A=211—1
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Ta có A = 2A - A
= \(2\left(1+2+2^2+2^3+...+2^{10}\right)\)- \(\left(1+2+2^2+2^3+....+2^{10}\right)\)
=\(2+2^2+2^3+2^4+.....+2^{11}\)\(-1-2-2^2-2^3-...-2^{10}\)
=\(2^{11}-1\)(Các số còn lại đã trừ hết cho nhau)
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Xem thêm câu trả lời
rút gọn:
A=\(x-4-\sqrt{16-8x^2+x^4}\left(x>4\right)\)
B=\(\dfrac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\left(a,b>0,a\ne b\right)\)
\(A=x-4-\sqrt{x^4-8x^2+16}=x-4-\sqrt{[\left(x-2\right)\left(x+2\right)]^2}\)
\(A=x-4-\left(x-2\right)\left(x+2\right)=x-4-\left(x^2-4\right)=-x^2+x\)
\(B=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}.\left(\sqrt{a}+\sqrt{b}\right)=a-b\)
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Rút gọn:
a.(x2-2)(-x+3)
\(\left(x^2-2\right)\left(-x+3\right)\)
\(=-x^3+3x^2+2x-6\)
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Rút gọn:
A=sinx.cos3x + sin7x.cos5x
B=cosx.cos4x + sin2x.sin3x
\(A=\dfrac{1}{2}sin4x-\dfrac{1}{2}sin2x+\dfrac{1}{2}sin12x+\dfrac{1}{2}sin2x\)
\(=\dfrac{1}{2}sin4x+\dfrac{1}{2}sin12x=sin8x.cos4x\)
\(B=\dfrac{1}{2}cos5x+\dfrac{1}{2}cos3x+\dfrac{1}{2}cosx-\dfrac{1}{2}cos5x\)
\(=\dfrac{1}{2}cos3x+\dfrac{1}{2}cosx=cos2x.cosx\)
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Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Rút gọn:
A= \(\dfrac{10\sqrt{x}}{x+3\sqrt{x}-4}\) - \(\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}\) + \(\dfrac{\sqrt{x}+1}{1-\sqrt{x}}\) ( với x ≥ 0; x ≠ 1)
Với `x >= 0,x ne 1` có:
`A=[10\sqrt{x}]/[(\sqrt{x}-1)(\sqrt{x}+4)]-[2\sqrt{x}-3]/[\sqrt{x}+4]-[\sqrt{x}+1]/[\sqrt{x}-1]`
`A=[10\sqrt{x}-(2\sqrt{x}-3)(\sqrt{x}-1)-(\sqrt{x}+1)(\sqrt{x}+4)]/[(\sqrt{x}-1)(\sqrt{x}+4)]`
`A=[10\sqrt{x}-2x+2\sqrt{x}+3\sqrt{x}-3-x-4\sqrt{x}-\sqrt{x}-4]/[(\sqrt{x}-1)(\sqrt{x}+4)]`
`A=[-3x+10\sqrt{x}-7]/[(\sqrt{x}-1)(\sqrt{x}+4)]`
`A=[(\sqrt{x}-1)(-3\sqrt{x}-7)]/[(\sqrt{x}-1)(\sqrt{x}+4)]`
`A=[-3\sqrt{x}-7]/[\sqrt{x}+4]`
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rút gọn:A=1.2+2.3+3.4+......+2015.2016
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+............+2015.2016.(2017-2014)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.............+2015.2016.2017-2014.2015.2016
3A=2015.2016.2017
A=2015.2016.2017:3
A=2015.672.2017
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Rút gọn:
A=\(\dfrac{3-\sqrt{3} }{\sqrt{3}-1 } \)
\(A=\dfrac{\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=\sqrt{3}\)
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