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\(A=136^2-92.136+46^2=136^2-2.136.46+46^2=\left(136-46\right)^2=90^2=8100\)\(B=135^2+110.135+55^2=135^2+2.135.55+55^2=\left(135+55\right)^2=190^2=36100\)
b) \(263^2+74.263+37^2\)
\(=\left(263+37\right)^2\)
\(=300^2\)
\(=90000\)
c) \(136^2-92.136+46^2\)
\(=\left(136-46\right)^2\)
\(=90^2\)
\(=8100\)
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
Tính giá trị biểu thức sau:
a, A= \(258^2-\dfrac{242^2}{254^2}-246^2\approx\) 6047,1
b, B= \(263^2+74.263+37^2=90000\)
c, C= \(136^2-92.136+46^2=8100\)
d, D = \(\left(50^2+48^2+46^2+...+2^2\right)-\left(49^2+47^2+45^2+...+1^2\right)\)
= 22100 - 20825= 1275
\(\frac{258^2-242^2}{254^2-246^2}=\frac{\left(258+242\right)\left(258-242\right)}{\left(254+246\right)\left(254-246\right)}=\frac{500.16}{500.8}=2\)
\(263^2+74.263+37^2=263^2+2.37.263+37^2=\left(263+37\right)^2=300^2=90000\)
\(136^2-92.136+46^2=136^2-46.2.136+46^2=\left(136-46\right)^2=90^2=8100\)
\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+.....+\left(2^2-1^2\right)=\left(50+49\right)\left(50-49\right)+\left(48+47\right)\left(48-47\right)+....+\left(2+1\right)\left(2-1\right)=\left(50+49+....+1\right)=\frac{51.50}{2}=51.25=1275\)
46 . 2 = 92 nhỉ?
\(F=136^2-92.136+46^2=136^2-2.46.136+46^2=\left(136-46\right)^2=90^2=8100\)
Tính hợp lí:
F = 1362 − 92.136 + 462
F = 1362 − 2.46.136 + 462
F = (136 + 46)2
\(\Rightarrow\) Áp dụng hằng đẳng thức số 2: (A - B)2 = A2 - 2AB + B2
1362 − 92.136 + 462
= 1362 − 2.46.136 + 462
=(136−46)2
=902
=8100