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Bài 1:
\(\frac{97^3+83^3}{180}-97\cdot83=\frac{\left(97+83\right)\left(97^2-97\cdot83+83^2\right)}{180}-97\cdot83\)
\(=97^2-97\cdot83+83^2-97\cdot83=97^2-2\cdot97\cdot83+83^2\)
\(=\left(97-83\right)^2=14^2=196\)
Bài 2:
\(x^2-10x=-25\)
\(\Leftrightarrow x^2-10x+25=0\)
\(\Leftrightarrow\left(x-5\right)^2=0\)
\(\Leftrightarrow x-5=0\Leftrightarrow x=5\)
\(C=\frac{97^3+83^3}{180}-97.83\)
\(C=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)
\(C=\frac{180\left(97^2-97.83+83^2\right)}{180}-97.83\)
\(C=97^2-97.83+83^2-97.83\)
\(C=97^2-2.97.83+83^2\)
\(C=\left(97-83\right)^2=14^2=196\)
\(R=\frac{43^2-11^2}{\left(36,5\right)^2-\left(27,5\right)^2}\)
\(=\frac{\left(43-11\right)\left(43+11\right)}{\left(36,5-27,5\right)\left(36,5+27,5\right)}\)
\(=\frac{32.54}{9.64}\)
\(=\frac{6}{2}=3\)
Bạn viết sai đề bài rồi
\(S=\frac{97^3+83^3}{180}-97.83\)
\(=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)
\(=97^2-97.83+83-97.83\)
\(=\left(97-83\right)^2=14^2=196\)
Trả lời:
\(R=\frac{43^2-11^2}{36,5^2-27,5^2}\)
\(R=\frac{\left(43-11\right).\left(43+11\right)}{\left(36,5-27,5\right).\left(36,5+27,5\right)}\)
\(R=\frac{32.54}{9.64}\)
\(R=3\)
Đề bài sai bạn nhé
\(S=\frac{97^3+83^3}{180}-97.83\)
\(S=\frac{\left(97+83\right).\left(97^2-97.23+83^2\right)}{180}-97.83\)
\(S=97^2-97.83+83^2-97.83\)
\(S=97^2-2.97.83+83^2\)
\(S=\left(97-83\right)^2\)
\(S=14^2\)
\(S=196\)
Với a,b >0.Ta có: \(\frac{1}{a}+\frac{1}{b}\ge\frac{\left(1+1\right)^2}{a+b}=\frac{4}{a+b}\left(đpcm\right)\)
Dấu = xảy ra khi và chỉ khi a=b
\(a,\frac{97^3+83^3}{180}-97.83\)
\(=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)
\(=\frac{180\left(97^2-97.83+83^2\right)}{180}-97.83\)
\(=97^2-97.83+83^2-97.83\)
\(=97^2+83^2-2.97.83\)
\(=\left(97-83\right)^2\)
\(=14^2=196\)