Question

[Pham Văn Hiếu]

Tính nhẩm

a 26²+52.24 +24²

b 52² + 47²+94.53

c 50²-49² +48²-47²+...+2²-1²

d 87²+ 26 .87+13²

e 3003²-3²

f 85.12,7+5.3.12,7

Answer 1

[Hà Linh]

a) \(26^2+52.24+24^2=26^2+2.26.24+24^2\)

= \(\left(26+24\right)^2=50^2=2500\)

b) \(52^2+47^2+94.52\) ( câu này sai đề sửa luôn)

= \(52^2+2.47.52+47^2=\left(52+47\right)^2=99^2\)

= \(9801\)

c) \(50^2-49^2+48^2-47^2+...+2^2-1^2\)

= \(\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)

= \(99+95+...+3\)

Dãy số này có : \(\dfrac{99-3}{4}+1=\dfrac{96}{4}+1=25\) số hạng

\(\Rightarrow\) \(99+95+...+3\) = \(\left(99+3\right).25:2=1275\)

d) \(87^2+26.87+13^2=87^2+2.13.87+13^2\)

\(=\left(87+13\right)^2=100^2=10000\)

e) \(3003^2-3^2=\left(3003-3\right)\left(3003+3\right)\)

= \(3000.3006=9018000\)

Answer 2

[Mới vô]

\(a,26^2+52\cdot24+24^2\\ =26^2+2\cdot26\cdot24+24^2\\ =\left(26+24\right)^2\\ =50^2\\ =2500\)

\(b,53^2+47^2+94\cdot53\\ =53^2+2\cdot47\cdot53+47^2\\ =\left(53+47\right)^2\\ =100^2\\ =10000\)

\(c,50^2-49^2+48^2-47^2+...+2^2-1^2\\ =\left(50+49\right)\left(50-49\right)+\left(48+47\right)\left(48-47\right)+...+\left(2+1\right)\left(2-1\right)\\ =99\cdot1+97\cdot1+...+3\cdot1\\ =99+97+...+3\\ \)

\(99+97+...+3\) có số số hạng là \(\dfrac{99-3}{2}+1=49\)(số)

\(\Rightarrow99+97+...+3=\dfrac{\left(99+3\right)\cdot49}{2}=2499\)

\(d,87^2+26\cdot87+13^2\\ =87^2+2\cdot13\cdot87+13^2\\ =\left(87+13\right)^2\\ =100^2\\ =10000\)

\(e,3003^2-3^2\\ =\left(3003+3\right)\left(3003-3\right)\\ =3006\cdot3000\\ =9018000\)

\(f,85\cdot12,7+5\cdot3\cdot12,7\\ =85\cdot12,7+15\cdot12,7\\ =12,7\cdot\left(85+15\right)\\ =12,7\cdot100\\ =1270\)

\(\text{Chúc bạn học tốt}\)