Question

Find value of a nap b when 3✓5/3+2✓5 = a✓5 -1/11b

Answer 1

Answer:

a=(-30) and b=$(-\frac{9}{11})$

Step-by-step explanation:

$\frac{3\sqrt{5} }{3+2\sqrt{5} }=a\sqrt{5}-\frac{1}{11b}$

Solving LHS by Rationalising the Denominator:-

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

$\frac{9\sqrt{5}-30 }{(3)^2-(2\sqrt{5})^2 }$

$\frac{-(30-9\sqrt{5}) }{9-20}$

$\frac{-(30-9\sqrt{5}) }{-(11)}$

$\frac{30-9\sqrt{5} }{11}$

$\frac{30}{11}-\frac{9\sqrt{5} }{11}$

Comparing Both LHS and RHS,we get:-

a=(-30) and b=$(-\frac{9}{11})$