Question

If root 2 + root 3 by 3 root 2 minus 2 root 3 is equal to a + b root 6 find the value of a and b

Answer 1

Answer:

$a=0\:and\:b=\frac{1}{6}$

Step-by-step explanation:

$Given \:\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}=a+b\sqrt{6}$

$LHS=\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}\\=\frac{(\sqrt{2}+\sqrt{3})(3\sqrt{2}-2\sqrt{3})}{(3\sqrt{2}+2\sqrt{3})(3\sqrt{2}-2\sqrt{3}}\\=\frac{\sqrt{2}(3\sqrt{2}-2\sqrt{3})+\sqrt{3}(3\sqrt{2}-2\sqrt{3})}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$

$=\frac{6-2\sqrt{6}+3\sqrt{6}-6}{18-12}$

$=\frac{\sqrt{6}}{6}$

$0+\frac{\sqrt{6}}{6}=a+b\sqrt{6}\:(By\:RHS)$

$a=0\:and\:b=\frac{1}{6}$

Therefore,

$a=0\:and\:b=\frac{1}{6}$

•••♪

Answer 2

Answer:

a=2 and b=5

please find your answer in the above attached pic