Question

3-root 5/(3+2 root 5) = a root 5 - b what are values of a and b

Answer 1

Answer:

$\huge\boxed{\bigstar\:\:\:a=(-3)\:and\:b=(-1)\:\:\:\bigstar}$

Step-by-step explanation:

✼ Given:-

• $\frac{3-\sqrt{5} }{3+2\sqrt{5} }=a\sqrt{5} -b$

✼ To Find:-

   The Values of a and b.

✼ Solution:-

→ Solving RHS:-

$\implies\frac{(3-\sqrt{5})(3-2\sqrt{5}) }{(3+2\sqrt{5})(3-2\sqrt{5}) }$

$\implies\frac{9-10+6\sqrt{5}-3\sqrt{5} }{(3)^2-(2\sqrt{5})^2 }$

$\implies\frac{3\sqrt{5}-1 }{9-10 }$

$\implies\frac{-(1-3\sqrt{5}) }{-(1) }$

$\implies 1-3\sqrt{5}$

Now we know that,

$\implies\frac{3-\sqrt{5} }{3+2\sqrt{5} }=a\sqrt{5} -b$

$\implies 1-3\sqrt{5} =a\sqrt{5} -b$

By Substituting the Values of a and b, we get

→ $-3\sqrt{5} =a\sqrt{5}$

→ $\large\boxed{a=(-3)}$

→ $-b=1$

→ $\large\boxed{b=(-1)}$

Answer 2

✉️

-probably you

b= -1

a= -3