Question

√5+√3÷2√5-3√3=a-b√15 thenbfind a and b

Answer 1

Answer:  The required values of a and b are

$a=-\dfrac{19}{7},~~b=\dfrac{5}{7}.$

Step-by-step explanation:  We are given to find the values of a and b from the following :

$\dfrac{\sqrt5+\sqrt3}{2\sqrt5-3\sqrt3}=a-b\sqrt{15}~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To find the required values of a and b, we need to rationalize the denominator on the L.H.S. of (i).

From equation (i), we have

$\dfrac{\sqrt5+\sqrt3}{2\sqrt5-3\sqrt3}=a-b\sqrt{15}\\\\\\\Rightarrow \dfrac{(\sqrt5+\sqrt3)(2\sqrt5+3\sqrt3)}{(2\sqrt5-3\sqrt3)(2\sqrt5+3\sqrt3)}=a-b\sqrt{15}\\\\\\\Rightarrow \dfrac{2\times5+3\sqrt{3\times5}+2\sqrt{3\times5}+3\times3}{(2\sqrt5)^2-(3\sqrt3)^2}=a-b\sqrt{15}\\\\\\\Rightarrow \dfrac{19+5\sqrt{15}}{20-27}=a-b\sqrt{15}\\\\\\\Rightarrow -\dfrac{19}{7}-\dfrac{5}{7}\sqrt{15}=a-b\sqrt{15}.$

Comparing the corresponding coefficients in the above equation, we get

$a=-\dfrac{19}{7},~~b=\dfrac{5}{7}.$

Thus, the required values of a and b are

$a=-\dfrac{19}{7},~~b=\dfrac{5}{7}.$

Answer 2

Answer:

answer is a=+-19/7

b=5/7