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\(=\left(80-75\right)\left(80+75\right)+\left(70-65\right)\left(75+65\right)+...+\left(10-5\right)\left(10+5\right)\)
\(=5\cdot155+5\cdot135+..+5\cdot15\)
\(=5\cdot\left(155+135+...+15\right)\)
\(=5\cdot\left(155+15+135+35+115+55+95+75\right)\)
\(=5\cdot\left(170\cdot4\right)\)
\(=5\cdot680=3400\)
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1+2+3+4+5+6+7+8+9= 45
2+2+2+2+2+2+2+2+2+2= 20
10+20+30+49+50+60+70+80+90= 459
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vì x=5+y => x-y=5
đặt \(A=x^2+y\left(y-2x\right)+75\)
\(=x^2+y^2-2xy+75\)
\(=\left(x-y\right)^2+75\)
\(=5^2+75\)
=100
b) đặt \(B=x\left(x+2\right)+y\left(y-2\right)-2xy+65\)
\(=x^2+2x+y^2-2y-2xy+65\)
\(=\left(x^2+y^2-2xy\right)+\left(2x-2y\right)+65\)
\(=\left(x-y\right)^2+2\left(x-y\right)+65\)
\(=5^2+2.5+65\)
=100
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a) \(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)
\(=\left(85^2-15^2\right)+\left(75^2-25^2\right)+\left(65^2-35^2\right)+\left(55^2-45^2\right)\)
\(=\left(85-15\right)\left(85+15\right)+\left(75-25\right)\left(75+25\right)+\left(65-35\right)\left(65+35\right)+\left(55-45\right)\left(55+45\right)\)
\(=70.100+50.100+30.100+10.100\)
\(=7000+5000+3000+1000\)
\(=16000\)
b) \(\frac{135^2+130.135+65^2}{135^2-65^2}\)
\(=\frac{135^2+2.60.135+65^2}{135^2-65^2}\)
\(=\frac{\left(135+65\right)^2}{\left(135-65\right)^2}\)
\(=\frac{200^2}{70^2}\) \(=\frac{200}{70}=\frac{20}{7}\)
Bài làm:
Ta có: \(80^2-75^2+70^2-65^2+60^2-...+10^2-5^2\)
\(=\left(80-75\right)\left(80+75\right)+\left(70-65\right)\left(70+65\right)+...+\left(10-5\right)\left(10+5\right)\)
\(=5.\left(80+75\right)+5.\left(70+65\right)+...+5.\left(10+5\right)\)
\(=5.\left(80+75+70+65+...+10+5\right)\)
\(=5\cdot\frac{\left(5+80\right)\cdot\left[\left(80-5\right)\div5+1\right]}{2}\)
\(=5\cdot\frac{85\cdot16}{2}=3400\)