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B1:
\(a.301^2=\left(300+1\right)^2=300^2+2.300.1+1^2\\ =90000+600+1=90601\\ b.88^2+2.88.12+12^2=\left(88+12\right)^2=100^2=10000\\ c.99.100=100^2-100=10000-100=9900\\ d,153^2+94.153+47^2=153^2+2.153.47+47^2=\left(153+47\right)^2=200^2=40000\)
B2:
\(A=x^2-20x+101\\ =x^2-2.x.10+10^2+1\\ =\left(x-10\right)^2+1\ge1\forall x\in R\left(Vì:\left(x-10\right)^2\ge0\forall x\in R\right)\\ \Rightarrow min_A=1\Leftrightarrow x-10=0\Leftrightarrow x=10\)
\(156^2-124^2+44^2-24^2+156+88+248\cdot24\)
\(=156^2+44^2+156+88-\left(124-24\right)^2\)
\(=26515-10000\)
=16515
Lời giải:
$A=64^2-54^2=(64-54)(64+54)=10.118=1180$
$B=76^2+2.76.23+23^2=(76+23)^2=99^2=(100-1)^2=100^2-2.100+1$
$=10000-200+1=9801$
$C=88^2+62^2-38^2-12^2=(88^2-38^2)+(62^2-12^2)$
$=(88-38)(88+38)+(62-12)(62+12)$
$=50.126+50.74=50(126+74)=50.200=10000$
\(x^3-3x^2y+3xy^2-y^3\)
\(=\left(x-y\right)^3\)
Thay \(x=88\) và \(y=-12\) vào biểu thức trên, ta được:
\(\left[88-\left(-12\right)\right]^3\)
\(=\left(88+12\right)^3\)
\(=100^3\)
\(=1000000\)
#Urushi☕
\(\frac{x-96}{2}+\frac{x-88}{4}+\frac{x-76}{6}+\frac{x-60}{8}=14\)
\(\frac{x-96}{2}-2+\frac{x-88}{4}-3+\frac{x-76}{6}-4+\frac{x-60}{8}-5=0\)
\(\frac{x-96}{2}-\frac{4}{2}+\frac{x-88}{4}-\frac{12}{4}+\frac{x-76}{6}-\frac{24}{6}+\frac{x-60}{8}-\frac{40}{8}=0\)
\(\frac{x-96-4}{2}+\frac{x-88-12}{4}+\frac{x-76-24}{6}+\frac{x-60-40}{8}=0\)
\(\frac{x-100}{2}+\frac{x-100}{4}+\frac{x-100}{6}+\frac{x-100}{8}=0\)
\((x-100)\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)=0\)
\(\Rightarrow x-100=0\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}>0\right)\)
\(\Rightarrow x=100\)
1492281077
= 1492281077394
k mk nha