a: \(A=\dfrac{\left(258-242\right)\left(258+242\right)}{\left(254-246\right)\left(254+246\right)}=\dfrac{16}{8}=2\)

b: \(=\left(263+37\right)^2=300^2=90000\)

c: \(=\left(136-46\right)^2=90^2=8100\)

d: \(=50^2-49^2+48^2-47^2+...+2^2-1^2\)

=50+49+...+2+1

=51x50:2=1275

b) \(263^2+74.263+37^2\)

\(=\left(263+37\right)^2\)

\(=300^2\)

\(=90000\)

c) \(136^2-92.136+46^2\)

\(=\left(136-46\right)^2\)

\(=90^2\)

\(=8100\)

cảm ơn lê tài bảo châu nhé

\(\frac{63^2-47^2}{215^2-105^2}=\)  \(\frac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}\)

                           \(=\frac{16.110}{110.320}=\frac{16}{320}\)\(=\frac{1}{20}\)

các câu kia làm tương tự nha

Thanks bạn nhiều nhiều nha!

nhưng câu d với câu e mk khô hiểu lắm!

Bài 3:

a) \(\left|x-2\right|+9y^2+12xy+4x^2=0\)

\(\Leftrightarrow\left|x-2\right|+\left(3y+2x\right)^2=0\)

Dễ thấy \(VT\ge0\forall x;y\)

\(\Rightarrow\left\{{}\begin{matrix}x-2=0\\3y+2x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=\frac{-4}{3}\end{matrix}\right.\)

Vậy...

b) \(3x^2+y^2+10x-2xy+26=0\)

\(\Leftrightarrow x^2-2xy+y^2+2x^2+10x+26=0\)

\(\Leftrightarrow\left(x-y\right)^2+2\left(x^2+5x+\frac{25}{4}\right)+\frac{27}{2}=0\)

\(\Leftrightarrow\left(x-y\right)^2+2\left(x+\frac{5}{2}\right)^2=\frac{-27}{2}\)

Dễ thấy \(VT\ge0\forall x;y\) mặt khác \(VP< 0\)

Do đó pt vô nghiệm

Bài 2:

\(A=263^2+74\cdot263+37^2\)

\(A=263^2+2\cdot263\cdot37+37^2\)

\(A=\left(263+37\right)^2\)

\(A=300^2\)

\(A=90000\)

b) tương tự

\(C=-1^2+2^2-3^2+...-99^2+100^2\)

\(C=\left(2^2-1^2\right)+\left(4^2-3^2\right)+...+\left(100^2-99^2\right)\)

\(C=\left(2-1\right)\left(1+2\right)+\left(4-3\right)\left(3+4\right)+...+\left(100-99\right)\left(99+100\right)\)

\(C=1+2+3+4+...+99+100\)

\(C=\frac{\left(100+1\right)\cdot100}{2}=5050\)

\(D=\left(3+1\right)\left(3^2+1\right)...\left(3^{32}+1\right)\)

\(2D=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)...\left(3^{32}+1\right)\)

\(2D=\left(3^2-1\right)\left(3^2+1\right)...\left(3^{32}+1\right)\)

\(2D=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{32}+1\right)\)

\(2D=\left(3^8-1\right)\left(3^8+1\right)...\left(3^{32}+1\right)\)

\(2D=\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(2D=\left(3^{32}-1\right)\left(3^{32}+1\right)\)

\(2D=3^{64}-1\)

\(D=\frac{3^{64}-1}{2}\)

\(263^2+74.263+37^2\)

\(=69169+74.263+1369\)

\(=69169+19462+1369\)

\(=88631+1369\)

\(=90000\)

B1: a) \(\left|x-2\right|+9y^2+12xy+4x^2=0\)

=> \(\left|x-2\right|+\left(3y+2x\right)^2=0\)

Ta có: \(\left|x-2\right|\ge0\forall x\)

         \(\left(3y+2x\right)^2\ge0\forall x;y\)

=> \(\left|x-2\right|+\left(3y+2x\right)^2\ge0\forall x;y\)

Dấu "=" xảy ra khi: \(\hept{\begin{cases}x-2=0\\3y+2x=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\3y=-2x\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\3y=-2.2=-4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\y=-\frac{4}{3}\end{cases}}\)

Vậy ...

\(A=263^2+74.263+37^2\)

\(=263^2+2.263.37+37^2\)

\(=\left(263+37\right)^2\)

\(=300^2=90000\)

\(B=136^2-92.136+46^2\)

\(=136^2-2.136.46+46^2\)

\(=\left(136-46\right)^2\)

\(=90^2=8100\)

\(263^2+74.263+37^2=263^2+2.37.263+37^2=\left(263+37\right)^2=300^2=90000\)

Áp dụng hằng đẳng thức thức 1: (a+b)²=a²+2ab+b²

Cảm ơn bạn rất nhiều!