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Bài 1:
\(\left(3\sqrt{2}+4\sqrt{3}\right)^2-\left(2\sqrt{2}+3\sqrt{3}\right)^2\)
\(=\left(3\sqrt{2}\right)^2+2\cdot3\sqrt{2}\cdot4\sqrt{3}+\left(4\sqrt{3}\right)^2-\left(2\sqrt{2}\right)^2-2\cdot2\sqrt{2}\cdot3\sqrt{3}-\left(3\sqrt{3}\right)^2\)
\(=18+24\sqrt{6}+48-8-12\sqrt{6}-27\)
\(=12\sqrt{6}+31\)
Bạn ơi! Bạn thử bấm đề vào máy tính bỏ túi đi ạ, nó không ra kết quả giống với kết quả của bạn là sao? Mình cũng đã làm giống bạn nhưng kết quả không giống nên mới đăng bài hỏi.
a) \(\sqrt{12}-3\sqrt{75}+0,5\sqrt{\left(-6\right)^2\cdot3}\)
\(=2\sqrt{3}-15\sqrt{3}+0,5\sqrt{108}\)
\(=-13\sqrt{3}+3\sqrt{3}\)
\(=-10\sqrt{3}\)
b) \(3\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}-\sqrt{4+2\sqrt{3}}\)
\(=3\left|\sqrt{2}-\sqrt{3}\right|-\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=3\left(\sqrt{3}-\sqrt{2}\right)-\left|\sqrt{3}+1\right|\)
\(=3\sqrt{3}-3\sqrt{2}-\sqrt{3}-1\)
\(=2\sqrt{3}-3\sqrt{2}-1\)
c) \(\left(\frac{2x+1}{x\sqrt{x}-1}-\frac{\sqrt{x}}{x+\sqrt{x}+1}\right)\div\frac{1}{x-2\sqrt{x}+1}\)
\(=\frac{2x+1-\left(\sqrt{x}-1\right)\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\div\frac{1}{\left(\sqrt{x}-1\right)^2}\)
\(=\frac{2x+1-x+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\left(\sqrt{x}-1\right)^2\)
\(=\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\left(\sqrt{x}-1\right)^2\)
\(=\sqrt{x}-1\)
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right)\sqrt{9-x^2}}\)
\(=\frac{\left(x+2\right)\left(x+3\right)+x\sqrt{\left(3-x\right)\left(3+x\right)}}{x\left(3-x\right)+\left(x+2\right)\sqrt{\left(3-x\right)\left(3+x\right)}}\)
\(=\frac{\left(x+2\right)\left(x+3\right)+x\sqrt{\left(3-x\right)\left(3+x\right)}}{x\left(3-x\right)+\left(x+2\right)\sqrt{\left(3-x\right)\left(3+x\right)}}\)
\(=\frac{\sqrt{3+x}\left(\left(x+2\right)\sqrt{x+3}+x\sqrt{3-x}\right)}{\sqrt{3-x}\left(\left(x+2\right)\sqrt{x+3}+x\sqrt{3-x}\right)}\)
\(=\frac{\sqrt{3+x}}{\sqrt{3-x}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right)\sqrt{x^2-6x+8}}\)
\(=\frac{\left(x-3\right)\left(x-2\right)+3\sqrt{\left(x-4\right)\left(x-2\right)}}{3\left(x-4\right)+\left(x-3\right)\sqrt{\left(x-4\right)\left(x-2\right)}}\)
\(=\frac{\sqrt{x-2}\left(\left(x-3\right)\sqrt{x-2}+3\sqrt{x-4}\right)}{\sqrt{x-4}\left(3\sqrt{x-4}+\left(x-3\right)\sqrt{x-2}\right)}\)
\(=\frac{\sqrt{x-2}}{\sqrt{x-4}}\)
Bài 1:
a, (Xin được sửa đề bài) \(C=\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x+1-4\sqrt{x-3}}\)
\(=\sqrt{x-3-2\sqrt{x-3}+1}-\sqrt{x-3-4\sqrt{x-3}+4}\)
\(=\sqrt{\left(\sqrt{x-3}-1\right)^2}-\sqrt{\left(\sqrt{x-3}-2\right)^2}\)
\(=\sqrt{x-3}-1-\sqrt{x-3}+2=1\)
b, \(D=\sqrt{m^2}-\sqrt{m^2-10m+25}\)
\(=m-\sqrt{\left(m-5\right)^2}\)
\(=m-m+5=5\)
Bài 2:
a, \(VT=\sqrt{x+2\sqrt{x-2}-1}.\left(\sqrt{x-2}-1\right):\left(\sqrt{x}-\sqrt{3}\right)\)
\(=\sqrt{x-2+2\sqrt{x-2}+1}.\left(\sqrt{x-2}-1\right):\left(\sqrt{x}-\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{x-2}+1\right)^2}.\left(\sqrt{x-2}-1\right):\left(\sqrt{x}-\sqrt{3}\right)\)
\(=\left(\sqrt{x-2}-1\right)\left(\sqrt{x-2}+1\right):\left(\sqrt{x}-\sqrt{3}\right)\)
\(=\left(x-3\right):\left(\sqrt{x}-\sqrt{3}\right)\)
\(=\sqrt{x}+\sqrt{3}=VP\)
b, \(VT=\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a+1-2\sqrt{a}}\)
\(=\left(\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)
\(=\left(\frac{\sqrt{a}-1+\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)^2}\right):\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)
\(=\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)^2}:\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)
\(=\frac{\left(\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)
\(=\frac{\sqrt{a}-1}{\sqrt{a}}=VP\)
Bài 1:
\(=18+48+2\cdot3\sqrt{2}\cdot4\sqrt{3}-8-27-2\cdot2\sqrt{2}\cdot3\sqrt{3}\)
=18+48-27-8
=10+21
=31
Bài 2:
\(\dfrac{x-\sqrt{x}-12}{3\sqrt{x}-12}=\dfrac{\left(\sqrt{x}-4\right)\left(\sqrt{x}+3\right)}{3\cdot\left(\sqrt{x}-4\right)}=\dfrac{\sqrt{x}+3}{3}\)