\((\frac23x-3):(-10)=\frac25\)
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4: Sửa đề: \(x=\sqrt[3]{3+2\sqrt2}-\sqrt[3]{3-2\sqrt2}\)
=>\(x^3=3+2\sqrt2-\left(3-2\sqrt2\right)+3\cdot x\cdot\sqrt[3]{\left(3+2\sqrt2\right)\left(3-2\sqrt2\right)}\)
=>\(x^3=6+3\cdot x\cdot1=3x+6\)
\(y=\sqrt[3]{17+12\sqrt2}-\sqrt[3]{17-12\sqrt2}\)
=>\(y^3=17+12\sqrt2-\left(17-12\sqrt2\right)-3\cdot y\cdot\sqrt[3]{\left(17+12\sqrt2\right)\left(17-12\sqrt2\right)}\)
=>\(y^3=34-3y\)
\(H=\left(x-y\right)^3+3\left(x-y\right)\left(xy+1\right)\)
\(=\left(x-y\right)\left(x^2-2xy+y^2+3xy+3\right)=\left(x-y\right)\left(x^2+xy+y^2+3\right)\)
\(=\left(x^3-y^3\right)+3\left(x-y\right)\)
=(3x+6-34+3y)+3x-3y
=3x+3y+3x-3y-28
=6x-28
Bài 3:
a: \(A=\sqrt{13+30\cdot\sqrt{2+\sqrt{9+4\sqrt2}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\sqrt{8+2\cdot2\sqrt2\cdot1+1}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\sqrt{\left(2\sqrt2+1\right)^2}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\left(2\sqrt2+1\right)}}\)
\(=\sqrt{13+30\cdot\sqrt{2+2\sqrt2+1}}\)
\(=\sqrt{13+30\cdot\sqrt{\left(\sqrt2+1\right)^2}}\)
\(=\sqrt{13+30\cdot\left(\sqrt2+1\right)}=\sqrt{43+30\sqrt2}\)
\(=\sqrt{25+2\cdot5\cdot3\sqrt2+18}=\sqrt{\left(5+3\sqrt2\right)^2}=5+3\sqrt2\)
b: \(B=\frac{3+\sqrt5}{2\sqrt2+\sqrt{3+\sqrt5}}+\frac{3-\sqrt5}{2\sqrt2-\sqrt{3-\sqrt5}}\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt{6+2\sqrt5}}+\frac{3-\sqrt5}{4-\sqrt{6-2\sqrt5}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt{\left(\sqrt5+1\right)^2}}+\frac{3-\sqrt5}{4-\sqrt{\left(\sqrt5-1\right)^2}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\left(\sqrt5+1\right)^{}}+\frac{3-\sqrt5}{4-\left(\sqrt5-1\right)^{}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt5+1^{}}+\frac{3-\sqrt5}{4-\sqrt5+1^{}}\right)=\sqrt2\left(\frac{3+\sqrt5}{5+\sqrt5^{}}+\frac{3-\sqrt5}{5-\sqrt5^{}}\right)\)
\(=\frac{1}{\sqrt2}\left(\frac{2\left(3+\sqrt5\right)}{5+\sqrt5}+\frac{2\left(3-\sqrt5\right)}{5-\sqrt5}\right)=\frac{1}{\sqrt2}\cdot\left(\frac{6+2\sqrt5}{5+\sqrt5}+\frac{6-2\sqrt5}{5-\sqrt5}\right)\)
\(=\frac{1}{\sqrt2}\left(\frac{\left(\sqrt5+1\right)^2}{\sqrt5\left(\sqrt5+1\right)}+\frac{\left(\sqrt5-1\right)^2}{\sqrt5\left(\sqrt5-1\right)}\right)=\frac{1}{\sqrt2}\cdot\frac{\sqrt5+1+\sqrt5-1}{\sqrt5}=\frac{1}{\sqrt2}\cdot2=\sqrt2\)
c: \(C=\sqrt{4+\sqrt{10+2\sqrt5}}+\sqrt{4-\sqrt{10+2\sqrt5}}\)
=>\(C^2=4+\sqrt{10+2\sqrt5}+4-\sqrt{10+2\sqrt5}+2\cdot\sqrt{4^2-\left(10+2\sqrt5\right)}\)
=>\(C^2=8+2\cdot\sqrt{16-10-2\sqrt5}=8+2\cdot\sqrt{6-2\sqrt5}\)
=>\(C^2=8+2\cdot\left(\sqrt5-1\right)=6+2\sqrt5=\left(\sqrt5+1\right)^2\)
=>\(C=\sqrt5+1\)
f: \(F=\sqrt[3]{26+15\sqrt3}-\sqrt[3]{26-15\sqrt3}\)
\(=\sqrt[3]{2^3+3\cdot2^2\cdot\sqrt3+3\cdot2\cdot\left(\sqrt3\right)^2+3\sqrt3}-\sqrt[3]{2^3-3\cdot2^2\cdot\sqrt3+3\cdot2\cdot\left(\sqrt3\right)^2-3\sqrt3}\)
\(=\sqrt[3]{\left(2+\sqrt3\right)^3}-\sqrt[3]{\left(2-\sqrt3\right)^3}=2+\sqrt3-\left(2-\sqrt3\right)=2\sqrt3\)
4: Sửa đề: \(x=\sqrt[3]{3+2\sqrt2}-\sqrt[3]{3-2\sqrt2}\)
=>\(x^3=3+2\sqrt2-\left(3-2\sqrt2\right)+3\cdot x\cdot\sqrt[3]{\left(3+2\sqrt2\right)\left(3-2\sqrt2\right)}\)
=>\(x^3=6+3\cdot x\cdot1=3x+6\)
\(y=\sqrt[3]{17+12\sqrt2}-\sqrt[3]{17-12\sqrt2}\)
=>\(y^3=17+12\sqrt2-\left(17-12\sqrt2\right)-3\cdot y\cdot\sqrt[3]{\left(17+12\sqrt2\right)\left(17-12\sqrt2\right)}\)
=>\(y^3=34-3y\)
\(H=\left(x-y\right)^3+3\left(x-y\right)\left(xy+1\right)\)
\(=\left(x-y\right)\left(x^2-2xy+y^2+3xy+3\right)=\left(x-y\right)\left(x^2+xy+y^2+3\right)\)
\(=\left(x^3-y^3\right)+3\left(x-y\right)\)
=(3x+6-34+3y)+3x-3y
=3x+3y+3x-3y-28
=6x-28
Bài 3:
a: \(A=\sqrt{13+30\cdot\sqrt{2+\sqrt{9+4\sqrt2}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\sqrt{8+2\cdot2\sqrt2\cdot1+1}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\sqrt{\left(2\sqrt2+1\right)^2}}}\)
\(=\sqrt{13+30\cdot\sqrt{2+\left(2\sqrt2+1\right)}}\)
\(=\sqrt{13+30\cdot\sqrt{2+2\sqrt2+1}}\)
\(=\sqrt{13+30\cdot\sqrt{\left(\sqrt2+1\right)^2}}\)
\(=\sqrt{13+30\cdot\left(\sqrt2+1\right)}=\sqrt{43+30\sqrt2}\)
\(=\sqrt{25+2\cdot5\cdot3\sqrt2+18}=\sqrt{\left(5+3\sqrt2\right)^2}=5+3\sqrt2\)
b: \(B=\frac{3+\sqrt5}{2\sqrt2+\sqrt{3+\sqrt5}}+\frac{3-\sqrt5}{2\sqrt2-\sqrt{3-\sqrt5}}\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt{6+2\sqrt5}}+\frac{3-\sqrt5}{4-\sqrt{6-2\sqrt5}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt{\left(\sqrt5+1\right)^2}}+\frac{3-\sqrt5}{4-\sqrt{\left(\sqrt5-1\right)^2}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\left(\sqrt5+1\right)^{}}+\frac{3-\sqrt5}{4-\left(\sqrt5-1\right)^{}}\right)\)
\(=\sqrt2\left(\frac{3+\sqrt5}{4+\sqrt5+1^{}}+\frac{3-\sqrt5}{4-\sqrt5+1^{}}\right)=\sqrt2\left(\frac{3+\sqrt5}{5+\sqrt5^{}}+\frac{3-\sqrt5}{5-\sqrt5^{}}\right)\)
\(=\frac{1}{\sqrt2}\left(\frac{2\left(3+\sqrt5\right)}{5+\sqrt5}+\frac{2\left(3-\sqrt5\right)}{5-\sqrt5}\right)=\frac{1}{\sqrt2}\cdot\left(\frac{6+2\sqrt5}{5+\sqrt5}+\frac{6-2\sqrt5}{5-\sqrt5}\right)\)
\(=\frac{1}{\sqrt2}\left(\frac{\left(\sqrt5+1\right)^2}{\sqrt5\left(\sqrt5+1\right)}+\frac{\left(\sqrt5-1\right)^2}{\sqrt5\left(\sqrt5-1\right)}\right)=\frac{1}{\sqrt2}\cdot\frac{\sqrt5+1+\sqrt5-1}{\sqrt5}=\frac{1}{\sqrt2}\cdot2=\sqrt2\)
c: \(C=\sqrt{4+\sqrt{10+2\sqrt5}}+\sqrt{4-\sqrt{10+2\sqrt5}}\)
=>\(C^2=4+\sqrt{10+2\sqrt5}+4-\sqrt{10+2\sqrt5}+2\cdot\sqrt{4^2-\left(10+2\sqrt5\right)}\)
=>\(C^2=8+2\cdot\sqrt{16-10-2\sqrt5}=8+2\cdot\sqrt{6-2\sqrt5}\)
=>\(C^2=8+2\cdot\left(\sqrt5-1\right)=6+2\sqrt5=\left(\sqrt5+1\right)^2\)
=>\(C=\sqrt5+1\)
f: \(F=\sqrt[3]{26+15\sqrt3}-\sqrt[3]{26-15\sqrt3}\)
\(=\sqrt[3]{2^3+3\cdot2^2\cdot\sqrt3+3\cdot2\cdot\left(\sqrt3\right)^2+3\sqrt3}-\sqrt[3]{2^3-3\cdot2^2\cdot\sqrt3+3\cdot2\cdot\left(\sqrt3\right)^2-3\sqrt3}\)
\(=\sqrt[3]{\left(2+\sqrt3\right)^3}-\sqrt[3]{\left(2-\sqrt3\right)^3}=2+\sqrt3-\left(2-\sqrt3\right)=2\sqrt3\)
ko nên làm
Nửa chu vi hình chữ nhật:
80 : 2 = 40 (cm)
Chiều rộng hình chữ nhật:
80 . 1 : 10 = 8 (cm)
Chiều dài hình chữ nhật:
40 - 8 = 32 (cm)
Diện tích hình chữ nhật:
32 . 8 = 256 (cm²)
Chiều rộng hình hộp đó là:
80:10=8(cm)
Nửa chu vi hình chữ nhật là:
80:2=40(cm)
Chiều dài hình chữ nhật đó là :
40-8=32(cm)
Diện tích hình chữ nhật đó là:
32 x 8=256(cm^2)
Vậy né chứ mình ko bit đúng hay sai đâu☺️☺️☺️
Bạn ấn vào tên hiển thị của người bạn cần tìm là có thể vảo trang cá nhân rồi.
Chúc bạn học tốt!
\(\left(\frac23x-3\right):\left(-10\right)=\frac25\)
\(\frac23x-3=\frac25\cdot\left(-10\right)\)
\(\frac23x-3=\frac{2\cdot\left(-10\right)}{5}\)
\(\frac23x-3=-\frac{20}{5}=-4\)
\(\frac23x=-4+3\)
\(\frac23x=1\)
\(x=1:\frac23\)
\(x=1\cdot\frac32\)
\(x=\frac32\)
Vậy \(x=\frac32\)
\(\left(\frac23x-3\right):\left(-10\right)=\frac25\)
\(\frac23x-3=-4\)
\(\frac23x=-1\)
\(x=-\frac32=-1,5\)
Vậy \(x=-1,5\)