Toán Lớp 9: Thực hiện phép tính
a.1/3-căn5 – 1/căn5-1
b.1/căn5+1 + 1/căn5-2 – 1/3-căn5 – căn5
c.(15/căn6+1 + 4/căn6 -2 -12/3-căn6) x (căn6+11)
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 9: Thực hiện phép tính
a.1/3-căn5 – 1/căn5-1
b.1/căn5+1 + 1/căn5-2 – 1/3-căn5 – căn5
c.(15/căn6+1 + 4/căn6 -2 -12/3-căn6) x (căn6+11)
Comments ( 2 )
a)\dfrac{1}{{3 – \sqrt 5 }} – \dfrac{1}{{\sqrt 5 – 1}}\\
= \dfrac{{3 + \sqrt 5 }}{{{3^2} – 5}} – \dfrac{{\sqrt 5 + 1}}{{5 – 1}}\\
= \dfrac{{3 + \sqrt 5 }}{4} – \dfrac{{\sqrt 5 + 1}}{4}\\
= \dfrac{2}{4} = \dfrac{1}{2}\\
b)\dfrac{1}{{\sqrt 5 + 1}} + \dfrac{1}{{\sqrt 5 – 2}} – \dfrac{1}{{3 – \sqrt 5 }} – \sqrt 5 \\
= \dfrac{{\sqrt 5 – 1}}{{5 – 1}} + \dfrac{{\sqrt 5 + 2}}{{5 – 4}} – \dfrac{{3 + \sqrt 5 }}{{9 – 5}} – \sqrt 5 \\
= \dfrac{{\sqrt 5 – 1}}{4} + \sqrt 5 + 2 – \dfrac{{3 + \sqrt 5 }}{4} – \sqrt 5 \\
= \dfrac{{\sqrt 5 – 1 – 3 – \sqrt 5 }}{4} + 2\\
= \dfrac{{ – 4}}{4} + 2\\
= 1\\
c)\left( {\dfrac{{15}}{{\sqrt 6 + 1}} + \dfrac{4}{{\sqrt 6 – 2}} – \dfrac{{12}}{{3 – \sqrt 6 }}} \right).\left( {\sqrt 6 + 11} \right)\\
= \left( {\dfrac{{15\left( {\sqrt 6 – 1} \right)}}{{6 – 1}} + \dfrac{{4\left( {\sqrt 6 + 2} \right)}}{{6 – 4}} – \dfrac{{12\left( {3 + \sqrt 6 } \right)}}{{9 – 6}}} \right).\left( {\sqrt 6 + 11} \right)\\
= \left( {3\sqrt 6 – 3 + 2\sqrt 6 + 4 – 12 – 4\sqrt 6 } \right).\left( {\sqrt 6 + 11} \right)\\
= \left( {\sqrt 6 – 11} \right)\left( {\sqrt 6 + 11} \right)\\
= 6 – {11^2}\\
= – 115
\end{array}$