CHO \(a=\frac{1}{2}\sqrt{\left(\sqrt{2}+\frac{1}{8}\right)}-\frac{\sqrt{2}}{8}\)
TÍNH \(S=a^2+\sqrt{a^4+a+1}\)
Những câu hỏi liên quan
Rút gọn
a) \(\left(\frac{2+\sqrt{a}}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right)\left(\frac{a\sqrt{a}-\sqrt{a}-1}{\sqrt{a}}\right)\)
b) \(\left(\frac{\sqrt{x}+1}{x-4}-\frac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\left(\frac{x\sqrt{x}+2x+4\sqrt{x}-8}{\sqrt{x}}\right)\)
1 Rút gọn:
a) Afrac{sqrt[]{2+sqrt[]{3}}}{4}+sqrt[]{frac{2-sqrt[]{3}}{16}}+frac{1}{sqrt[]{3}+sqrt[]{2}+1}
b)left(sqrt[]{a+sqrt[]{a^2-8}}right).left(sqrt[]{a-2sqrt[]{2}}-sqrt[]{a+2sqrt[]{2}}right),a2sqrt[]{2}
2.Cho x sqrt[]{2-sqrt[]{3}}.left(sqrt[]{6}+sqrt[]{2}right)-frac{2sqrt[]{6}+sqrt[]{3}}{sqrt[]{8}+1}. Tính A x^5-3x^4-3x^3+6x^2-20x+2022
3. Cho a,b,c 0, frac{a}{a+b}frac{b}{c+a}frac{c}{a+b}. CMR: frac{left(a+bright)^3}{c^3}+frac{left(b+cright)^3}{a^3}+frac{left(a+cright)^3}{b^3}+24
Đọc tiếp
1 Rút gọn:
a) A=\(\frac{\sqrt[]{2+\sqrt[]{3}}}{4}+\sqrt[]{\frac{2-\sqrt[]{3}}{16}}+\frac{1}{\sqrt[]{3}+\sqrt[]{2}+1}\)
b)\(\left(\sqrt[]{a+\sqrt[]{a^2-8}}\right).\left(\sqrt[]{a-2\sqrt[]{2}}-\sqrt[]{a+2\sqrt[]{2}}\right),a>=2\sqrt[]{2}\)
2.Cho x= \(\sqrt[]{2-\sqrt[]{3}}.\left(\sqrt[]{6}+\sqrt[]{2}\right)-\frac{2\sqrt[]{6}+\sqrt[]{3}}{\sqrt[]{8}+1}\). Tính A= \(x^5-3x^4-3x^3+6x^2-20x+2022\)
3. Cho a,b,c >0, \(\frac{a}{a+b}=\frac{b}{c+a}=\frac{c}{a+b}\). CMR: \(\frac{\left(a+b\right)^3}{c^3}+\frac{\left(b+c\right)^3}{a^3}+\frac{\left(a+c\right)^3}{b^3}+24\)
. Chứng minh đẳng thức
a) \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}=\sqrt{2}-1\) b) \(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\frac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}=1\)
Rút gọn biểu thức:
a) A frac{sqrt{5-2sqrt{6}}+sqrt{8-2sqrt{15}}}{sqrt{7+2sqrt{10}}}
b) B left(1+frac{a+sqrt{a}}{sqrt{a}+1}right).left(1-frac{a-sqrt{a}}{sqrt{a}-1}right) a0 va a # 1
c) C frac{asqrt{a}-8+2a-4sqrt{a}}{a-4}
d) D frac{1}{2a-1}.sqrt{5a^4.left(-4a+4a^2right)}
e) E frac{2}{x^2-y^2}.sqrt{frac{3x^2+6xy+3y^2}{4}}
Đọc tiếp
Rút gọn biểu thức:
a) A = \(\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
b) B = \(\left(1+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right).\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\) a>0 va a # 1
c) C = \(\frac{a\sqrt{a}-8+2a-4\sqrt{a}}{a-4}\)
d) D = \(\frac{1}{2a-1}.\sqrt{5a^4.\left(-4a+4a^2\right)}\)
e) E = \(\frac{2}{x^2-y^2}.\sqrt{\frac{3x^2+6xy+3y^2}{4}}\)
B1 Cho biểu thức A=\(\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{x-3}{x+2\sqrt{x}+4}-\frac{\sqrt{x}+7}{x\sqrt{x}-8}\right):\left(\frac{\sqrt{x}+7}{x+2\sqrt{x}+4}\right)\)
1, Rút gọn A. Tìm x sao cho A<2
2, Cho 1≤a,b,c≤2. Chứng minh rằng \(\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\le10\)
Cho \(x=\sqrt{6+2\sqrt{2}.\left(\sqrt{\frac{5}{2}-\sqrt{6}+\sqrt{\left(3\sqrt{a}+1\right)\left(2a-2\right)-\frac{6a^2+6\sqrt{a}-8a-4a\sqrt{a}}{\sqrt{a}-1}+8}}\right)}\) với a là số thực không âm
\(y=\frac{\frac{x-2}{x}+\frac{1}{x-2}}{12-8\sqrt{5}}.\left(-16\right)\)
So sánh x và y
Rút gọn A = \(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right) :\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
a, Rút gọn A b , Tìm x thỏa mãn A > 1 c,Tính A với \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)
a
\(\sqrt{25-3\sqrt{\frac{4}{3}}}\)
b\(\left(-2^3\right)+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)
c\(\left(-2^2\right)+\sqrt{36}.2-\sqrt{9}.3+\sqrt{25}\)
Cho biểu thức P=\(\left(\frac{\sqrt{x-1}}{3+\sqrt{x-1}}+\frac{x+8}{10-x}\right):\left(\frac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\frac{1}{\sqrt{x-1}}\right)\)
a) Rút gọn P
b) Tính giá trị của P khi \(x=\sqrt[4]{\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}-\sqrt[4]{\frac{3-2\sqrt{2}}{3+2\sqrt{2}}}\)