Trục căn thức ở mẫu và thực hiện phép tính
1) $\frac{7}{2√3}$
2) $\frac{√5 + 1}{√5-1}$
3) ( $\frac{2}{√3-1}$ + $\frac{3}{√3-2}$ + $\frac{15}{3-√3}$). $\frac{1}{√3+5}$
4)
$\frac{3}{√5-√2}$ – $\frac{2}{2-√2}$ + $\frac{1}{√3+√2}$
Trục căn thức ở mẫu và thực hiện phép tính
1) $\frac{7}{2√3}$
2) $\frac{√5 + 1}{√5-1}$
3) ( $\frac{2}{√3-1}$ + $\frac{3}{√3-2}$ + $\frac{15}{3-√3}$). $\frac{1}{√3+5}$
4)
$\frac{3}{√5-√2}$ – $\frac{2}{2-√2}$ + $\frac{1}{√3+√2}$
Đáp án:
Giải thích các bước giải:
1)7/2√3 =7.√3/2.√3.√3=7√3/6
2)√5+1/√5 -1
=(√5+1).(√5+1) /(√5-1).(√5+1)
=(√5+1)²/5-1
=(√5+1)²/4
=( (√5+1) /2)²
3) ( 2/√3-1 +3/√3-2 +15/ √3-3) .1/√3+5
=( 2.(√3+1)/(√3+1).(√3-1) +3.(√3+2)/(√3+2).(√3-2) +15.(√3+3)/(√3+3).(√3-3) ).1/√3+5
=(2(√3+1)/2 +3.(√3+2)/-1 +15.(√3+3)/-6 ) .1/√3+5
=( √3+1 -3√3 -6 -5/2.√3 -15/2 ). √3-5/(√3+5).(√3-5)
=( -2√3 -5/2.(√3-1) ). √3 -5/-22
=2√3.(√3-5)/22 +5/2.(√3-1).(√3 -5)/22
=3 -5.√3 /11 +5/2.( 3-6√3 +5)/22
=3 -5.√3 /11 +15/2 -15√3 +25/2 /22
=6 -10√3 +7,5 -15√3 +12,5 /22
=26 -25√3 /22
4)
3/√5 -√2 – 2 /2-√2 + 1/ √3 +√2
=3.(√5+√2)/3 – 2.(2 +√2)/4-2 +√3-√2/1
=√5 +√2 – 2 -√2 +√3 – √2
=√5 -2 -√2
1) $\dfrac{7}{2\sqrt{3}} = \dfrac{7.\sqrt{3}}{2\sqrt{3}.\sqrt{3}}$ $= \dfrac{7\sqrt{3}}{2.3} = \dfrac{7\sqrt{3}}{6}$
2) $\dfrac{\sqrt{5} + 1}{\sqrt{5} – 1} = \dfrac{(\sqrt{5} + 1)(\sqrt{5} + 1)}{(\sqrt{5} – 1)(\sqrt{5} + 1)}$
$= \dfrac{5 + 2\sqrt{5} + 1}{5 – 1} = \dfrac{2(3 + \sqrt{5})}{4}$ $= \dfrac{3 + \sqrt{5}}{2}$
3) $[\dfrac{2}{\sqrt{3} – 1} + \dfrac{3}{\sqrt{3} – 2} + \dfrac{15}{3 – \sqrt{3}}]. \dfrac{1}{\sqrt{3} + 5}$
$= [\dfrac{2(\sqrt{3} + 1}{2} + \dfrac{3(\sqrt{3} + 2)}{3 – 4} + \dfrac{15(3 + \sqrt{3})}{9 – 3}] . \dfrac{\sqrt{3} – 5}{(\sqrt{3} + 5})(\sqrt{3} – 5}$
$= (\sqrt{3} + 1 – 3\sqrt{3} – 2 + \dfrac{15 – 5\sqrt{3}}{2}) . \dfrac{\sqrt{3} – 5}{-2}$
$= – 2(\s
4) $\dfrac{3}{\sqrt{5} – \sqrt{2}} – \dfrac{2}{2 – \sqrt{2}} + \dfrac{1}{\sqrt{3} + \sqrt{2}}$
$= \dfrac{3(\sqrt{5} – \sqrt{2})(\sqrt{5} + \sqrt{2})} – \dfrac{2(2 + \sqrt{2})}{(2 – \sqrt{2})(2 + \sqrt{2})} + \dfrac{\sqrt{3} – \sqrt{2}}{(\sqrt{3} – \sqrt{2})(\sqrt{3} + \sqrt{2})}$
$= \sqrt{5} + \sqrt{2} – 2 – \sqrt{2} + \sqrt{3} + \sqrt{2}$
$= \sqrt{5} – 2 + \sqrt{3} + \sqrt{2}$