tolong bantu secepatnya yaalagi butuh banget iniisoal tentang bentuk akarmakasii yg udh jawabnote : .... Question from @disyahilmiya1206

September 2022 1 14 Report

tolong bantu secepatnya yaa
lagi butuh banget inii

soal tentang bentuk akar

makasii yg udh jawab

note : jawab dgn tepat + pake cara

klo gatau skip yaa ^^

JΟY

Merasionalkan bentuk ${\boldsymbol{\dfrac{\textsf{\textbf{a}}}{\textsf{\textbf{b}}\pm\sqrt{\textsf{\textbf{c}}}}}}$

Pembahasan

–› No. 1

$\begin{aligned}{\sf{\frac{3}{2-\sqrt{\sf7}}}}&={\sf{\frac{3}{2-\sqrt{\sf7}}\times\frac{2+\sqrt{\sf7}}{2+\sqrt{\sf7}}}}\\&={\sf{\frac{3\left(2+\sqrt{\sf7}\right)}{\left(2-\sqrt{\sf7}\right)\left(2+\sqrt{\sf7}\right)}}}\\&={\sf{\frac{3\left(2+\sqrt{\sf7}\right)}{4-7}}}\\&={\sf{\frac{\cancel3\left(2+\sqrt{\sf7}\right)}{-\cancel3}}}\\&={\sf{-\left(2+\sqrt{\sf7}\right)}}\\&={\sf{-2-\sqrt{\sf7}}}\end{aligned}$

–› No. 2

$\begin{aligned}{\sf{\frac{2}{5+\sqrt{\sf11}}}}&={\sf{\frac{2}{5+\sqrt{\sf11}}\times\frac{5-\sqrt{\sf11}}{5-\sqrt{\sf11}}}}\\&={\sf{\frac{2\left(5-\sqrt{\sf11}\right)}{\left(5+\sqrt{\sf11}\right)\left(5-\sqrt{\sf11}\right)}}}\\&={\sf{\frac{2\left(5-\sqrt{\sf11}\right)}{25-11}}}\\&={\sf{\frac{\cancel2\left(5-\sqrt{\sf11}\right)}{\cancel{14}}}}\\&={\sf{\frac{5-\sqrt{\sf11}}{7}}}\end{aligned}$

Sehingga dapat disimpulkan rumus

$\boxed{\begin{aligned}{\sf{I.~~\frac{a}{b-\sqrt{\sf{c}}}}}&={\sf{\frac{a}{b-\sqrt{\sf{c}}}\times\frac{b+\sqrt{\sf{c}}}{b+\sqrt{\sf{c}}}}}\\&={\sf{\frac{a\left(b+\sqrt{\sf{c}}\right)}{\left(b-\sqrt{\sf{c}}\right)\left(b+\sqrt{\sf{c}}\right)}}}\\&={\sf{\frac{a\left(b+\sqrt{\sf{c}}\right)}{b^2-c}}}\end{aligned}}$

$\boxed{\begin{aligned}{\sf{II.~~\frac{a}{b+\sqrt{\sf{c}}}}}&={\sf{\frac{a}{b+\sqrt{\sf{c}}}\times\frac{b-\sqrt{\sf{c}}}{b-\sqrt{\sf{c}}}}}\\&={\sf{\frac{a\left(b-\sqrt{\sf{c}}\right)}{\left(b+\sqrt{\sf{c}}\right)\left(b-\sqrt{\sf{c}}\right)}}}\\&={\sf{\frac{a\left(b-\sqrt{\sf{c}}\right)}{b^2-c}}}\end{aligned}}$