K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

11 tháng 7 2019

Sửa đề  CM:  \(\sqrt{11+6\sqrt{2}}=3+\sqrt{2}\)

Ta có: \(\sqrt{11+6\sqrt{2}}=\sqrt{3^2+2.3\sqrt{2}+2}=\sqrt{\left(3+\sqrt{2}\right)^2}=|3+\sqrt{2}|=3+\sqrt{2}\)

11 tháng 7 2019

#)Sửa đề : \(\left(3+\sqrt{2}\right)^2\)

#)Giải :

\(11+6\sqrt{2}=9+2.3.\sqrt{2}+2=\left(3+\sqrt{2}\right)^2\left(đpcm\right)\)

20 tháng 5 2019

a, phân tích vế trái ta được:

11+6\(\sqrt{2}\)=9+2.3.\(\sqrt{2}\)+2=(3+\(\sqrt{2}\))2\(\)=VP(dpcm)

b,phân tích vế trái ta được

\(\sqrt{11+6\sqrt{ }2}\)+\(\sqrt{11-6\sqrt{ }2}\)=|3+\(\sqrt{2}\)|+|3-\(\sqrt{2}\)|=6=VP(dpcm)

a,phân tích vế trái ta được

8-2\(\sqrt{7}\)=7-2\(\sqrt{7}\)+1=(\(\sqrt{7}\)-1)2

câu b sai đề nha

20 tháng 5 2019

Ta có a) \(11+6\sqrt{2}=9+2\times3\times\sqrt{2}+2=\left(3+\sqrt{2}\right)^2\)

b) \(\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}=\sqrt{\left(3+\sqrt{2}\right)^2}+\sqrt{\left(3-\sqrt{2}\right)^2}\)

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

NV
15 tháng 7 2021

\(B=\left(\dfrac{15\left(\sqrt{6}-1\right)}{\left(\sqrt{6}-1\right)\left(\sqrt{6}+1\right)}+\dfrac{4\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}-\dfrac{12\left(3+\sqrt{6}\right)}{\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\dfrac{15\left(\sqrt{6}-1\right)}{5}+\dfrac{4\left(\sqrt{6}+2\right)}{2}-\dfrac{12\left(3+\sqrt{6}\right)}{3}\right)\left(\sqrt{6}+11\right)\)

\(=\left[3\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)\right]\left(\sqrt{6}+11\right)\)

\(=\left(3\sqrt{6}-3+2\sqrt{6}+4-12-4\sqrt{6}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)\)

\(=6-121=-115\) là số nguyên (đpcm)

b) Ta có: \(B=\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\dfrac{15\left(\sqrt{6}-1\right)}{5}+\dfrac{4\left(\sqrt{6}+2\right)}{2}-\dfrac{12\left(3+\sqrt{6}\right)}{3}\right)\left(\sqrt{6}+11\right)\)

\(=\left(3\sqrt{6}-3+2\sqrt{6}+4-12-4\sqrt{6}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)\)

=6-121=-115

14 tháng 6 2018

a/ \(11+6\sqrt{2}=9+2\cdot3\cdot\sqrt{2}+2=\left(3+\sqrt{2}\right)^2\left(đpcm\right)\)

b/ \(8-2\sqrt{7}=\sqrt{7}^2-2\sqrt{7}\cdot1+1=\left(\sqrt{7}-1\right)^2\left(đpcm\right)\)

14 tháng 6 2018

Ta có:a)11+6\(\sqrt{2}\) =\(9+2.3.\sqrt{2}+2\) =\(3^2+2.3.\sqrt{2}+\left(\sqrt{2}\right)^2\)=\(\left(3+\sqrt{2}\right)^2\)

b) \(8-2\sqrt{7}\) = \(7-2.1.\sqrt{7}+1\) =\(\left(\sqrt{7}\right)^2-2.1.\sqrt{7}+1^2\) =\(\left(\sqrt{7}-1\right)^2\)

27 tháng 7 2023

Xem lại câu c) và d) 

b: =căn 10-3+4-căn 10=1

a: \(=\sqrt{11-4\sqrt{6}+\sqrt{15}}\)

 

27 tháng 7 2020

Trả lời:

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-12\sqrt{5}+9}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{5-2\sqrt{5}+1}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{5}+1}\)

\(A=\sqrt{1}\)

\(A=1\)

\(B=\frac{\left(5+2\sqrt{6}\right).\left(49-20\sqrt{6}\right).\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(3+2\sqrt{6}+2\right).\left(49-20\sqrt{6}\right).\sqrt{3-2\sqrt{6}+2}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right)^2.\left(49-20\sqrt{6}\right).\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right)^2.\left(49-20\sqrt{6}\right).\left(\sqrt{3}-\sqrt{2}\right)}{9\sqrt{33}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right).\left(49-20\sqrt{6}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(3-2\right).\left(49\sqrt{3}-60\sqrt{2}+49\sqrt{2}-40\sqrt{3}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{1.\left(9\sqrt{3}-11\sqrt{2}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=1\)

20 tháng 9 2020

a) Ta có: \(\sqrt{29-12\sqrt{5}}=\sqrt{20-12\sqrt{5}+9}=\sqrt{\left(2\sqrt{5}-3\right)^2}\)

\(=\left|2\sqrt{5}-3\right|=2\sqrt{5}-3\)

\(\Rightarrow\sqrt{3-\sqrt{29-12\sqrt{5}}}=\sqrt{3-\left(2\sqrt{5}-3\right)}=\sqrt{3-2\sqrt{5}+3}\)

\(=\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-1\right)^2}\)

\(=\left|\sqrt{5}-1\right|=\sqrt{5}-1\)

\(\Leftrightarrow A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}\)

\(=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\)( đpcm )

2 tháng 7 2016

tách bình phương ra

1: Chứng minh

a) Ta có: \(VT=11+6\sqrt{2}\)

\(=9+2\cdot3\cdot\sqrt{2}+2\)

\(=\left(3+\sqrt{2}\right)^2=VP\)(đpcm)

b) Ta có: \(VP=\left(\sqrt{7}-1\right)^2\)

\(=7-2\cdot\sqrt{7}\cdot1+1\)

\(=8-2\sqrt{7}=VT\)(đpcm)

c) Ta có: \(VT=\left(5-\sqrt{3}\right)^2\)

\(=25-2\cdot5\cdot\sqrt{3}+3\)

\(=28-10\sqrt{3}=VP\)(đpcm)

d) Ta có: \(VP=\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

\(=\sqrt{3+2\cdot\sqrt{3}\cdot1+1}-\sqrt{3-2\cdot\sqrt{3}\cdot1+1}\)

\(=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}\)

\(=\left|\sqrt{3}+1\right|-\left|\sqrt{3}-1\right|\)

\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)\)

\(=\sqrt{3}+1-\sqrt{3}+1\)

\(=2=VT\)(đpcm)

TL
28 tháng 7 2020

thêm dòng này nữa :33

⇔ 11 + \(6\sqrt{2}=11+6\sqrt{2}\left(đpcm\right)\)