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Tính nhanh:
a)
153^2 + 94 * 153 + 47^2
= 153 * (153 + 94) + 47^2
= 153 * 247 + 47^2
= 153 * (200 + 47) + 47^2
= 153 * 200 + 153 * 47 + 47^2
= 153 * 200 + 47 * (153 + 47)
= 153 * 200 + 47 * 200
= 200 * (153 + 47)
= 200 * 200
= 40000
b)126^2 - 152.126 + 5776
= 126 . 126 - 152.126 +126. 2888/63
= 126 . ( 126 - 152 + 2888/63)
= 126 . 1250/63
= 2500
Câu c bn tự làm nha
a) \(153^2+94.153+47^2=153^2+2.47.153+47^2\)
\(=\left(153+47\right)^2=200^2=40000\)
b) \(126^2-152.126+5776=126^2-2.76.126+76^2\)
\(=\left(126-76\right)^2=50^2=2500\)
c) \(3^8.5^8-\left(15^4-1\right)\left(15^4+1\right)=15^8-\left[\left(15^4\right)^2-1\right]\)
\(=15^8-\left(15^8-1\right)=15^8-15^8+1=1\)
A: \(135^2+94\cdot153+47^2=135^2\cdot2\cdot47+153\cdot47\)
\(=47\left(36450+153\right)=36603\cdot47=1720341\)
B: \(126^2-152\cdot126+5776=126^2-2\cdot126\cdot76+76^2=\left(126-76\right)^2=50^2=2500\)
C: \(3^8\cdot5^8-\left(15^4-1\right)\left(15^4+1\right)=15^8-\left(15^8-1\right)=15^8-15^8+1=1\)
a)\(\left(153+47\right)^2\)
b)\(\left(126-76\right)^2\)
c)\(15^8-15^8+1=1\)
2: a) \(x^2-6x+2018\)
\(=\left(x^2-6x+9\right)+2009\)
\(=\left(x-3\right)^2+2009\)
Vì \(\left(x-3\right)^2\ge0\forall x\) ; \(2009>0\) nên \(\left(x-3\right)^2+2009>0\forall x\)
Hay \(x^2-6x+2018>0\forall x\) \(\left(dpcm\right)\)
b) \(4x-x^2-5\)
\(=-\left(x^2-4x+5\right)\)
\(=-\left[\left(x^2-4x+4\right)+1\right]\)
\(=-\left(x-2\right)^2-1\)
Vì \(\left(x-2\right)^2\ge0\forall x\) nên \(-\left(x-2\right)^2\le0\forall x\)
\(\Rightarrow-\left(x-2\right)^2-1< 0\)
Hay \(4x-x^2-5< 0\forall x\) \(\left(dpcm\right)\)
Bài 3:
\(A=2\left(x^2-3x\right)=2\left(x^2-2.x.\frac{3}{2}+\frac{9}{4}-\frac{9}{4}\right)\)
\(=2\left(x-\frac{3}{2}\right)^2-\frac{9}{2}\ge-\frac{9}{2}\)
Đẳng thức xảy ra khi x = 3/2
\(B=\left(x^2-x+\frac{1}{4}\right)+\left(y^2+6y+9\right)+1\)
\(=\left(x-\frac{1}{2}\right)^2+\left(y+3\right)^2+1\ge1\)
Đẳng thức xảy ra khi x = 1/2 y = -3
Tính nhanh :
1262 - 152 x 126 + 5776
= 126 x 126 - 152 x 126 + 5776
= 126(126-152) + 5776
= -3276 + 5776
= 2500
\(126^2-152.126+5776\)
\(=126.126-152.126+5776\)
\(=126.\left(126-152\right)+5776\)
\(=126.\left(-26\right)+5776\)
\(=\left(-3276\right)+5776\)
\(=2500\)
Ai giúp mình làm bài này với. Mình cảm ơn nhiều.
a) 153^2+99.153+47^2
= 153^2+2.47.153+47^2
= (153+47)^2
=200^2
=40000
b) 126^2-152.126+5776
= 126^2-2.76.126+76^2
= (126-76)^2
= 50^2
= 2500
c)3^8.5^8-(15^4-1).(15^4+1)
= 15^8-[(15^4)^2-1^2]
= 15^8-15^8+1
=1
d) (2+1).(2^2+1).(2^4+1)...(2^32+1)+1
= 1.(2+1).(2^2+1).(2^4+1)...(2^32+1)+1
= (2-1).(2+1).(2+1).(2^4+1)...(2^32+1)+1
= (2^2-1).(2^2+1).(2^4+1)...(2^32+1)+1
= (2^4-1).(2^4+1)...(2^32+1)+1
= (2^8-1)...(2^32+1)+1
= (2^32-1).(2^32+1)+1
= 2^64-1+1
= 2^64