lagi butuh banget inii
soal tentang bentuk akar
makasii yg udh jawab
note : jawab dgn tepat + pake cara
klo gatau skip yaa ^^
Merasionalkan bentuk [tex]{\boldsymbol{\dfrac{\textsf{\textbf{a}}}{\textsf{\textbf{b}}\pm\sqrt{\textsf{\textbf{c}}}}}}[/tex]
Pembahasan
–› No. 1
[tex]\begin{aligned}{\sf{\frac{3}{2-\sqrt{\sf7}}}}&={\sf{\frac{3}{2-\sqrt{\sf7}}\times\frac{2+\sqrt{\sf7}}{2+\sqrt{\sf7}}}}\\&={\sf{\frac{3\left(2+\sqrt{\sf7}\right)}{\left(2-\sqrt{\sf7}\right)\left(2+\sqrt{\sf7}\right)}}}\\&={\sf{\frac{3\left(2+\sqrt{\sf7}\right)}{4-7}}}\\&={\sf{\frac{\cancel3\left(2+\sqrt{\sf7}\right)}{-\cancel3}}}\\&={\sf{-\left(2+\sqrt{\sf7}\right)}}\\&={\sf{-2-\sqrt{\sf7}}}\end{aligned}[/tex]
–› No. 2
[tex]\begin{aligned}{\sf{\frac{2}{5+\sqrt{\sf11}}}}&={\sf{\frac{2}{5+\sqrt{\sf11}}\times\frac{5-\sqrt{\sf11}}{5-\sqrt{\sf11}}}}\\&={\sf{\frac{2\left(5-\sqrt{\sf11}\right)}{\left(5+\sqrt{\sf11}\right)\left(5-\sqrt{\sf11}\right)}}}\\&={\sf{\frac{2\left(5-\sqrt{\sf11}\right)}{25-11}}}\\&={\sf{\frac{\cancel2\left(5-\sqrt{\sf11}\right)}{\cancel{14}}}}\\&={\sf{\frac{5-\sqrt{\sf11}}{7}}}\end{aligned}[/tex]
Sehingga dapat disimpulkan rumus
[tex]\boxed{\begin{aligned}{\sf{I.~~\frac{a}{b-\sqrt{\sf{c}}}}}&={\sf{\frac{a}{b-\sqrt{\sf{c}}}\times\frac{b+\sqrt{\sf{c}}}{b+\sqrt{\sf{c}}}}}\\&={\sf{\frac{a\left(b+\sqrt{\sf{c}}\right)}{\left(b-\sqrt{\sf{c}}\right)\left(b+\sqrt{\sf{c}}\right)}}}\\&={\sf{\frac{a\left(b+\sqrt{\sf{c}}\right)}{b^2-c}}}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}{\sf{II.~~\frac{a}{b+\sqrt{\sf{c}}}}}&={\sf{\frac{a}{b+\sqrt{\sf{c}}}\times\frac{b-\sqrt{\sf{c}}}{b-\sqrt{\sf{c}}}}}\\&={\sf{\frac{a\left(b-\sqrt{\sf{c}}\right)}{\left(b+\sqrt{\sf{c}}\right)\left(b-\sqrt{\sf{c}}\right)}}}\\&={\sf{\frac{a\left(b-\sqrt{\sf{c}}\right)}{b^2-c}}}\end{aligned}}[/tex]
