Question

Please solve tomorrow is my exam

Answer 1

Answer:

rationalizing  it

(√5-1)²/(5-1)=(5+1-2√5)/4=(6-2√5)/4=3/2+√5/2

hence a=3/2 and b=1/2

Step-by-step explanation:

Answer 2

$\displaystyle\longrightarrow\sf {\dfrac {\sqrt5-1}{\sqrt5+1}=a+b\sqrt5}$

$\quad$

$\displaystyle\longrightarrow\sf {\dfrac {(\sqrt5-1)(\sqrt5-1)}{(\sqrt5+1)(\sqrt5-1)}=a+b\sqrt5}$

$\quad$

$\displaystyle\longrightarrow\sf {\dfrac {(\sqrt5-1)^2}{(\sqrt5)^2-1^2}=a+b\sqrt5}$

$\quad$

$\displaystyle\longrightarrow\sf {\dfrac {6-2\sqrt5}{4}=a+b\sqrt5}$

$\quad$

$\displaystyle\longrightarrow\sf {\dfrac {3}{2}-\dfrac {1}{2}\sqrt5=a+b\sqrt5}$

$\quad$

$\displaystyle\Longrightarrow\sf {\underline {\underline {\big (a,\ b\big)=\left (\dfrac {3}{2},\ -\dfrac {1}{2}\right)}}}$