\(A=\left(\sqrt{x-\sqrt{50}}-\sqrt{x+\sqrt{50}}\right)\sqrt{x+\sqrt{x^2}-50}\)
Suy ra 
\(A^2=\left(\sqrt{x-\sqrt{50}}-\sqrt{x+\sqrt{50}}\right)^2\left(x+\sqrt{x^2-50}\right)\)
\(=\left(2x-2\sqrt{x^2-50}\right)\left(x+\sqrt{x^2-50}\right)\)
\(=2\left(x-\sqrt{x^2-50}\right)\left(x+\sqrt{x^2-50}\right)\)
\(=2\left(x^2-\left(\sqrt{x^2-50}\right)^2\right)=2\left(x^2-\left(x^2-50\right)\right)=100\).
Với \(x\ge50\) thì \(x-\sqrt{50}< x+\sqrt{50}\) hay \(\sqrt{x-\sqrt{50}}< \sqrt{x+\sqrt{50}}\).
Suy ra \(A< 0\) mà \(A^2=100\) hay \(A=-10\).

làm bừa thui,ai tích mình mình tích lại

Số số hạng là : 

Có số cặp là :

50 : 2 = 25 ( cặp )

Mỗi cặp có giá trị là :

99 - 97 = 2 

Tổng dãy trên là :

25 x 2 = 50

Đáp số : 50

a) \(2\sqrt{32}+3\sqrt{72}-7\sqrt{50}+\sqrt{2}\)

\(=2\cdot4\sqrt{2}+3\cdot6\sqrt{2}-7\cdot5\sqrt{2}+\sqrt{2}\)

\(=8\sqrt{2}+18\sqrt{2}-35\sqrt{2}+\sqrt{2}\)

\(=-8\sqrt{2}\) 

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

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

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

\(=1\)

c) \(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)

\(=\sqrt{3^2+2\cdot3\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}-3+\sqrt{2}\)

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

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

\(=2\sqrt{2}\)

d) \(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\)

\(=x-4+\sqrt{x^2-8x+16}\)

\(=x-4+\sqrt{\left(x-4\right)^2}\)

\(=x-4+\left|x-4\right|\)

\(=x-4+x-4\)

\(=2x-8\) 

e) \(\dfrac{1}{a-b}\sqrt{a^4\left(a-b\right)^2}\left(a< b\right)\)

\(=\dfrac{1}{a-b}\sqrt{\left[a^2\left(a-b\right)\right]^2}\)

\(=\dfrac{1}{a-b}\left|a^2\left(a-b\right)\right|\)

\(=\dfrac{-a^2\left(a-b\right)}{a-b}\)

\(=-a^2\)

giai giúp mình với

a: \(A=5\sqrt{2}-6\sqrt{2}+\sqrt{2}-1=-1\)

\(B=\dfrac{x\sqrt{x}+1-\left(x-1\right)\left(\sqrt{x}-1\right)}{x-1}\)

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

b: A=B

=>căn x=-căn x+1

=>căn x=1/2

=>x=1/4

\(a,A=-3\sqrt{8}+\sqrt{50}+\sqrt{\left(1-\sqrt{2}\right)^2}\)

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

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

\(=-1\)

Vậy \(A=-1\)

\(b,\)

\(=\left(\dfrac{5\sqrt{x}}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}\right)\)

\(=\left(\dfrac{5x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}\right)\)

\(=\left(\dfrac{\sqrt{x}\left(5\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}\right)\)

\(=\dfrac{5\sqrt{x}-1}{\sqrt{x}-1}.\dfrac{\sqrt{x}-1}{\sqrt{x}}\)

\(=\dfrac{5\sqrt{x}-1}{\sqrt{x}}\)

Vậy \(B=\dfrac{5\sqrt{x}-1}{\sqrt{x}}\left(đk:x>0,x\ne1\right)\)

\(=\dfrac{\sqrt{x}\left(x+2\sqrt{x}\right)+2\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)+50-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}\\ =\dfrac{x\sqrt{x}+2x+2x-50+50-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}\\ =\dfrac{x\sqrt{x}-5\sqrt{x}+4x}{2\sqrt{x}\left(\sqrt{x}+5\right)}=\dfrac{\sqrt{x}\left(x+4\sqrt{x}-5\right)}{2\sqrt{x}\left(\sqrt{x}+5\right)}\\ =\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+5\right)}{2\sqrt{x}\left(\sqrt{x}+5\right)}=\dfrac{\sqrt{x}-1}{2}\)

\(\dfrac{x+2\sqrt{x}}{2\sqrt{x}+10}+\dfrac{\sqrt{x}-5}{\sqrt{x}}+\dfrac{50-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}\left(đk:x>0\right)\)

\(=\dfrac{\sqrt{x}\left(x+2\sqrt{x}\right)+2\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)+50-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}\)

\(=\dfrac{x\sqrt{x}+2x+2x-50+50-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}=\dfrac{x\sqrt{x}+4x-5\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}+5\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+5\right)}{2\sqrt{x}\left(\sqrt{x}+5\right)}=\dfrac{\sqrt{x}-1}{2}\)

Bạn nên viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người hiểu đề của bạn hơn nhé.

kết quả = .......

ko biết :(((