Tính
a. 1 1 3 + 2 1 2 = ...
b. 3 2 5 - 1 1 10 = ...
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8507cm2
32m^2 217dm^2=320217
3/5 giờ 12 phút = 48 phút
\(\dfrac{3}{7}.\left(\dfrac{5-1}{4}\right)=\dfrac{3}{7}.1=\dfrac{3}{7}\)
\(\dfrac{11}{10}-\dfrac{6}{10}=\dfrac{5}{10}=\dfrac{1}{2}\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`(2x - 3)^2`
`= 4x^2 - 12x + 9`
`b,`
`(x + 1)^2`
`= x^2 + 2x + 1`
`c,`
`(2x + 5)(2x - 5)`
`= 4x^2 - 25`
`d,`
`(a + b - c)(a - b + c)`
`= a^2 - b^2 + bc - c^2 + cb`
`e,`
\((x + 1)^2 - 10(x + 1) + 25\)
`= x^2 + 2x + 1 - 10x - 10 + 25`
`= x^2 - 8x +16`
`@` `\text {Kaizuu lv uuu}`
`@` CT:
Bình phương của `1` tổng: `(A + B)^2 = A^2 + 2AB + B^2`
Bình phương của `1` hiệu: `(A - B)^2 = A^2 - 2AB + B^2`
`A^2 - B^2 = (A-B)(A+B)`
c: \(=\dfrac{3}{2}\cdot1-1-20=\dfrac{3}{2}-21=\dfrac{-39}{2}\)
a) \(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{6-3+2}{6}=\dfrac{1}{6}\)
\(b.\) \(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{6+10}{15}=\dfrac{16}{15}\)
\(c.\) \(\dfrac{7}{11}.\dfrac{3}{4}+\dfrac{7}{11}.\dfrac{1}{4}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{16}{44}=\dfrac{21+7+16}{44}=\dfrac{44}{44}=1\)
a/\(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)
b/\(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{16}{15}\)
`1`
`a, 1/2 +1/3= 3/6 + 2/6 =5/6`
`d, 1/3 +3/5= 5/15 + 9/15=14/15`
`c,4/5 +1/2= 8/10 + 5/10= 13/10`
`2`
`a,1/2 +1/4=2/4 +1/4=3/4`
`b, 2/3 +1/6 = 4/6+1/6=5/6`
`c, 7/12 +1/2=7/12+ 6/12= 13/12`
`3`
Giải
Cả `2` ngày đi tất cả số quãng đường là :
`1/4 +1/2 =1/4+ 2/4= 3/4 ( quãng đường)`
đ/s...
`@ yL`
a, \(1+\dfrac{3}{4}=\dfrac{7}{4}\)
b, \(\dfrac{4}{5}-\dfrac{3}{8}=\dfrac{32-15}{40}=\dfrac{17}{40}\)
c, \(1:\dfrac{2}{3}=\dfrac{1.3}{2}=\dfrac{3}{2}\)
d, \(\dfrac{2}{5}.\dfrac{5}{2}=1\)
Bài 1:
a: \(\sqrt{27}+\dfrac{1}{2}\sqrt{48}-\sqrt{108}\)
\(=3\sqrt{3}+\dfrac{1}{2}\cdot4\sqrt{3}-6\sqrt{3}\)
\(=-3\sqrt{3}+2\sqrt{3}=-\sqrt{3}\)
b: \(\left(\sqrt{14}-\sqrt{10}\right)\cdot\sqrt{6+\sqrt{35}}\)
\(=\left(\sqrt{7}-\sqrt{5}\right)\cdot\sqrt{2}\cdot\sqrt{6+\sqrt{35}}\)
\(=\left(\sqrt{7}-\sqrt{5}\right)\cdot\sqrt{12+2\sqrt{35}}\)
\(=\left(\sqrt{7}-\sqrt{5}\right)\cdot\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}\)
\(=\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)=7-5=2\)
c: \(\dfrac{\sqrt{15}+\sqrt{3}}{1+\sqrt{5}}-\dfrac{2}{\sqrt{3}-1}\)
\(=\dfrac{\sqrt{3}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}-\dfrac{2\left(\sqrt{3}+1\right)}{3-1}\)
\(=\sqrt{3}-\sqrt{3}-1=-1\)
Bài 2:
a: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >1\end{matrix}\right.\)
\(A=\dfrac{x-5}{x+2\sqrt{x}-3}+\dfrac{1}{\sqrt{x}+3}+\dfrac{2}{\sqrt{x}-1}\)
\(=\dfrac{x-5}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}+3}+\dfrac{2}{\sqrt{x}-1}\)
\(=\dfrac{x-5+\sqrt{x}-1+2\sqrt{x}+6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
b: A=2
=>\(\sqrt{x}=2\left(\sqrt{x}-1\right)\)
=>\(2\sqrt{x}-2=\sqrt{x}\)
=>\(\sqrt{x}=2\)
=>x=4(nhận)
c: Để A là số nguyên thì \(\sqrt{x}⋮\sqrt{x}-1\)
=>\(\sqrt{x}-1+1⋮\sqrt{x}-1\)
=>\(\sqrt{x}-1\inƯ\left(1\right)\)
=>\(\sqrt{x}-1\in\left\{1;-1\right\}\)
=>\(\sqrt{x}\in\left\{2;0\right\}\)
=>\(x\in\left\{4;0\right\}\)
\(a,\dfrac{1}{3}-\left(-1\dfrac{2}{5}\right)+\left(-3\dfrac{1}{4}\right)\\ =\dfrac{1}{3}-\left(-\dfrac{7}{5}\right)-\dfrac{13}{4}\\ =\dfrac{1}{3}+\dfrac{7}{5}-\dfrac{13}{4}\\ =\dfrac{20}{3\times20}+\dfrac{7\times12}{5\times12}-\dfrac{13\times15}{4\times15}\\ =\dfrac{20+84-195}{60}\\ =\dfrac{-91}{60}\)
\(b,\dfrac{5}{4}-\left(-3\dfrac{1}{2}\right)-\dfrac{7}{10}\\ =\dfrac{5}{4}+\dfrac{7}{2}-\dfrac{7}{10}\\ =\dfrac{5\times5}{4\times5}+\dfrac{7\times10}{2\times10}-\dfrac{7\times2}{10\times2}\\ =\dfrac{25+70-14}{20}\\ =\dfrac{81}{20}\)
\(c,\dfrac{3}{2}-\left[\left(-\dfrac{4}{7}-\left(\dfrac{1}{2}+\dfrac{5}{8}\right)\right)\right]\\ =\dfrac{3}{2}-\left[-\dfrac{4}{7}-\left(\dfrac{4}{8}+\dfrac{5}{8}\right)\right]\\ =\dfrac{3}{2}-\left(-\dfrac{4}{7}-\dfrac{9}{8}\right)\\ =\dfrac{3}{2}+\dfrac{4}{7}+\dfrac{9}{8}\\ =\dfrac{3\times28}{2\times28}+\dfrac{4\times8}{8\times7}+\dfrac{9\times7}{8\times7}\\ =\dfrac{84+32+63}{56}\\ =\dfrac{179}{56}\)
`@` `\text {Ans}`
`\downarrow`
`a,`
\(\dfrac{1}{3}-\left(-1\dfrac{2}{5}\right)+\left(-3\dfrac{1}{4}\right)\)
`= 1/3+7/5 - 13/4`
`= 26/15 - 13/4`
`= -91/60`
`b,`
\(\dfrac{5}{4}-\left(-3\dfrac{1}{2}\right)-\dfrac{7}{10}\)
`= 5/4+7/2 - 7/10`
`= 1,25 + 3,5 - 0,7`
`= 4,75 - 0,7`
`= 4,05`
`c,`
\(\dfrac{3}{2}-\left[\left(-\dfrac{4}{7}\right)-\left(\dfrac{1}{2}+\dfrac{5}{8}\right)\right]\)
`= 3/2 - [(-4/7) - 9/8]`
`= 3/2 - (-95/56)`
`= 179/56`