Hỏi đáp về Căn bậc hai - Đại số 9

Chứng minh biểu thức không phụ thuộc vào x

\(K=\sqrt{x}+\dfrac{\sqrt[3]{2-\sqrt{3}}\cdot\sqrt[6]{7+4\sqrt{3}}-x}{\sqrt[4]{9-4\sqrt{5}}\cdot\sqrt{2+\sqrt{5}}+\sqrt{x}}\)

a/ \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)

b/ \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

Giúp mk vs các bn

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2https:https:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.https:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.hoc247.nethttps:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.imagehttps:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.faqhttps:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.data2https:https://hoc247.net/image/faq/data2/710107_.https://hoc247.net/image/faq/data2/710107_.hoc247.nethttps://hoc247.net/image/faq/data2/710107_.imagehttps://hoc247.net/image/faq/data2/710107_.faqhttps://hoc247.net/image/faq/data2/710107_.data2https://hoc247.net/image/faq/data2/710107_.185200_.775362_. Cho đường tròn (O;R) có dây BC cố định( không đi qua O), A là điểm chính giữa cung nhỏ BC, E thuộc cung lớn BC. Kẻ AE cắt BC tại D. hạ CH vuông góc với AE tại H, CH cắt BE tại M, I là trung điểm của dây BC.

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Lm câu c,d

Tìm MAX:

P = \(\dfrac{\sqrt{x-2016}}{x+1}+\dfrac{\sqrt{x-2017}}{x-1}\)

Cho x, y là hai số thực dương sao cho x + y= 1

Chứng minh: \(\dfrac{x}{1-x^2}+\dfrac{y}{1-y^2}\ge\dfrac{4}{3}\)

1. Cho a, b, c > 0. CM:

\(\dfrac{a^3+b^3}{2ab}+\dfrac{b^3+c^3}{2bc}+\dfrac{c^3+a^3}{2ac}\ge a+b+c\)

2. Cho a, b, c, d là các số dương. CM:

\(\dfrac{a-b}{b+c}+\dfrac{b-c}{c+d}+\dfrac{c-d}{a+d}+\dfrac{d-a}{a+b}\ge0\)

Giai phuong trinh: \(\dfrac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\dfrac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)

tính A=\(\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{.......+\sqrt{2}}}}}\) với n số \(\sqrt{2}\)

Bài 1 : Thực hiện phép tính :

a ) \(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}\)

b ) \(5\sqrt{48}-4\sqrt{27}-2\sqrt{75}+\sqrt{108}\)

c ) \(\sqrt{12}+2\sqrt{75}-3\sqrt{48}-\frac{2}{7}\sqrt{147}\)

d ) \(\sqrt{\left(3+\sqrt{5}\right)^2}-\sqrt{9-4\sqrt{5}}\)

e ) \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right):\frac{\sqrt{5}+\sqrt{2}}{3}\)

f ) \(\sqrt{11-6\sqrt{2}}-\sqrt{3-2\sqrt{2}}\)

g ) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right):\sqrt{2}-\sqrt{5}\)

h ) \(\left(\sqrt{56}-2\sqrt{6}-\sqrt{14}\right)\sqrt{14}+\sqrt{84}\)

k ) \(\left(\frac{1}{1-\sqrt{3}}-\frac{1}{1+\sqrt{3}}\right).\left(\sqrt{3}-1\right)\)

l ) \(\sqrt{21+8\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)

m ) \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)

n ) \(\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)

Làm không nổi thì câu nào biết thì làm làm từ từ dần dần giúp nha các bạn

Tìm giá trị lớn nhất của: A= \(\dfrac{x}{2}\) + \(\sqrt{1-x-2x^2}\) với \(-1\le x\le\dfrac{1}{2}\)

mội người giúp mình với (có lời giải càng tốt )

Với mọi x, y, z >= 0 . Chứng minh rằng

\(\sqrt{x^2+1}+\sqrt{y^2+1}+\sqrt{z^2+1}\ge\sqrt{6\left(x+y+z\right)}\)

cho a,b,c>0. CMR:

\(a+b+c\ge3\sqrt[3]{abc}+\left(\sqrt{a}-\sqrt{b}\right)^2\)

Tinh GTNN

\(\sqrt{x-x+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}}\)

giải phương trình sau: \(2\sqrt{x^2-4}-3=6\sqrt{x-2}-\sqrt{x+2}\)

Gía trị của biểu thức \(A=\dfrac{x^2-x+1}{x}\) biết \(x^2-4x+1=0\) là

Với a,b,c,d thuộc Q thỏa mãn a+b+c+d=0. CMR x=\(\sqrt{\left(ab-cd\right)\left(bc-ad\right)\left(ca-bd\right)}\in Q\)

giải hệ phương trình: \(\left\{{}\begin{matrix}\sqrt[3]{x}+\sqrt[3]{y}=1\\x-y=9\end{matrix}\right.\) ( \(\sqrt[3]{x},\sqrt[3]{y}\) là các số nguyên )

Cm A là số tự nhiên

A=\(\sqrt{8000^2+8000^2.8001^2+8001^2}\)

1) GHPT \(\left\{{}\begin{matrix}\sqrt{x+1}+\sqrt{2-y}=\sqrt{3}\\\sqrt{2-x}+\sqrt{y+1}=\sqrt{3}\end{matrix}\right.\)

2) GPT \(7x^2+7x=\sqrt{\dfrac{4x+9}{28}}\)

3) tìm số dương x,y,z thỏa \(x+y+z=\sqrt{xy}+\sqrt{yz}+\sqrt{zx}=2016\)

cho tam giác ABC có chu vi bằng 2 .Kí hiệu a,b,c là độ dài ba cạnh của tam giác .tìm giá trị nhỏ nhất của biểu thức S=a/b+c-a + 4d/c+a-b +9c/a+b-c

cho ba số thực dương x, y, z thỏa mãn x²+y²=z². tìm giá trị nhỏ nhất của bt \(P=\left(1+\dfrac{z}{x}\right)\left(1+\dfrac{z}{y}\right)\)

Cho pt x² -2mx +m - 2 =0

Gọi x₁ x₂ là nghiệm của phương trình. tìm m của biểu thức M= \(\dfrac{-24}{x_1^2 + x_2^2 -6x_1x_2}\)

SS \(5000^2va4999.5001\)

Chp phương trình: \(\left(x-2\right)\left(x^2-2x+m+1\right)=0\)

a, Tìm m để p/t có đúng 2 nghiệm

b, Tìm m để p/t có đúng 3 nghiệm

So sánh C=\(\sqrt{6+\sqrt{6+\sqrt{6}}}+\sqrt{2+\sqrt{2+\sqrt{2}}}\) và D=5