Rút gọn A=(4/x-cănx + cănx/cănx -1):1/cănx -1
Cho bieu thuc A=(4x−x+xx−1)÷1x−1\left(\dfrac{4}{x-\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}-1}\right)\div\dfrac{1}{\sqrt{x}-1}(x−x4+x−1x)÷x−11
a/ Tim dieu kien cua x de bieu thuc A co gia tri xac dinh
b/ Rut gon A
c/ Tinh gia tri cua A khi x = 4−234-2\sqrt{3}4−23
d/ Tim gia tri nho nhat cua A
a. ĐKXĐ : x>1.
b. A=(4x−x+xx−1):1x−1=[4x(x−1)+xx−1].(x−1)=4+x.xx(x−1).(x−1)=4+xxA=\left(\dfrac{4}{x-\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}-1}\right):\dfrac{1}{\sqrt{x}-1}=\left[\dfrac{4}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}}{\sqrt{x}-1}\right].\left(\sqrt{x}-1\right)=\dfrac{4+\sqrt{x}.\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}.\left(\sqrt{x}-1\right)=\dfrac{4+x}{\sqrt{x}}A=(x−x4+x−1x):x−11=[x(x−1)4+x−1x].(x−1)=x(x−1)4+x.x.(x−1)=x4+x
c. Thay x=4−23x=4-2\sqrt{3}x=4−23 vào A, ta có:
A=4+4−234−23=8−23(3−1)2=8−233−1=(8−23)(3+1)3−1=83+8−6−232=2+632=2(1+33)2=1+33A=\dfrac{4+4-2\sqrt{3}}{\sqrt{4-2\sqrt{3}}}=\dfrac{8-2\sqrt{3}}{\sqrt{\left(\sqrt{3}-1\right)^2}}=\dfrac{8-2\sqrt{3}}{\sqrt{3}-1}=\dfrac{\left(8-2\sqrt{3}\right)\left(\sqrt{3}+1\right)}{3-1}=\dfrac{8\sqrt{3}+8-6-2\sqrt{3}}{2}=\dfrac{2+6\sqrt{3}}{2}=\dfrac{2\left(1+3\sqrt{3}\right)}{2}=1+3\sqrt{3}A=4−234+4−23=(3−1)28−23=3−18−23=3−1(8−23)(3+1)=283+8−6−23=22+63=22(1+33)=1+33
Vậy giá trị của A tại x=4−23x=4-2\sqrt{3}x=4−23 là 1+331+3\sqrt{3}1+33.
Rút gọn căn(3-căn2)-căn(3+căn2)
Rut gon :3−2−3+2\sqrt{3-\sqrt{2}}-\sqrt{3+\sqrt{2}}3−2−3+2
Rút gọn M=n^3+2n^2-1/n^3+2n^2+2n+1
Rut gon : M=n3+2n2−1n3+2n2+2n+1M=\dfrac{n^3+2n^2-1}{n^3+2n^2+2n+1}M=n3+2n2+2n+1n3+2n2−1
Rút gọn A=căn((1+a^2)(1+b^2)(1+c^2))
cho a, b, c thoa man ab+bc+ca =1
rut gon ve dang ko chua can cua A= (1+a2)(1+b2)(1+c2)\sqrt{\left(1+a^2\right)\left(1+b^2\right)\left(1+c^2\right)}(1+a2)(1+b2)(1+c2)
please
Rút gọn A=căn(4-căn7)-căn(4+căn7)+căn7
giai giups nhanh nha,RUT GON
A=4−7−4+7+7\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}4−7−4+7+7
B=6.5+12+6.5−12+26\sqrt{6.5+\sqrt{12}}+\sqrt{6.5-\sqrt{12}}+2\sqrt{6}6.5+12+6.5−12+26
C=46+65−29−125\sqrt{46+\sqrt{6\sqrt{5}}}-\sqrt{29-12\sqrt{5}}46+65−29−125
D=13−160−53+490\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}13−160−53+490
Rút gọn A=căn(9a^2-12a+4)-9a+1
cho minh hoi(rut gon)
A=9a2−12a+4−9a+1\sqrt{9a^2-12a+4}-9a+19a2−12a+4−9a+1
Rút gọn B=cănx/cănx +4 + 4/cănx - 4): x+16/cănx +2
Cho cac bieu thuc :
A=x+4x+2,B=(xx+4+4x−4):x+16x+2A=\dfrac{\sqrt{x}+4}{\sqrt{x}+2},B=\left(\dfrac{\sqrt{x}}{\sqrt{x}+4}+\dfrac{4}{\sqrt{x}-4}\right):\dfrac{x+16}{\sqrt{x}+2}A=x+2x+4,B=(x+4x+x−44):x+2x+16
a) Rut gon B ?
b) Tim cac gia tri nguyen cua x de cac gia tri cua bieu thuc B(A-1) la so nguyen.
Rút gọn biểu thức 3căn8- 4 căn18 +5 căn32 - căn 50
rút gọn biểu thức
a) 38−418+532−503\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}38−418+532−50
b) (1550+5200−345015\sqrt{50}+5\sqrt{200}-3\sqrt{450}1550+5200−3450) : 10
c) 228+263−3175+1122\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}228+263−3175+112
d) (14−32\sqrt{14}-3\sqrt{2}14−32)2^22 +6286\sqrt{28}628
e) (1−2018)2\sqrt{\left(1-\sqrt{2018}\right)^2}(1−2018)2. 2019+22018\sqrt{2019+2\sqrt{2018}}2019+22018
f) (6−5)2−120\left(\sqrt{6}-\sqrt{5}\right)^2-\sqrt{120}(6−5)2−120
g)12(23−32)2+26+3412\left(2\sqrt{3}-3\sqrt{2}\right)^2+2\sqrt{6}+3\sqrt{4}12(23−32)2+26+34
Tính T=x căn(1+y^2)+ y căn(1+x^2)
Cho x×y+(1+x2)(1+y2)=2018x\times y+\sqrt{\left(1+x^2\right)\left(1+y^2\right)}=2018x×y+(1+x2)(1+y2)=2018 . Tính T=x1+y2+y1+x2T=x\sqrt{1+y^2}+y\sqrt{1+x^2}T=x1+y2+y1+x2 .
Tính 5+7 căn5/căn5 + 11 +căn11/1+căn11
5+755+11+111+11\dfrac{5+7\sqrt{5}}{\sqrt{5}}+\dfrac{11+\sqrt{11}}{1+\sqrt{11}}55+75+1+1111+11
Rút gọn căn12 - căn 27 + căn48/1- căn5 +căn(9-4 căn5)
a) Rút gọn 12−27+481−5+9−45\dfrac{\sqrt{12}-\sqrt{27}+\sqrt{48}}{1-\sqrt{5}+\sqrt{9-4\sqrt{5}}}1−5+9−4512−27+48
b) Giải hệ phương trình {x6−y6=1∣x+y∣+∣x−y∣=2\left\{{}\begin{matrix}x^6-y^6=1\\\left|x+y\right|+\left|x-y\right|=2\end{matrix}\right.{x6−y6=1∣x+y∣+∣x−y∣=2