Question

what is the value of x ?

Answer 1

Hope it helps! Just find the value of a and b then substitute it in the next equation and solve for x.

Answer 2

Answer:

The value of x is 3

Step-by-step explanation:

Given $\frac{4\sqrt{3}+5\sqrt{2}}{\sqrt{48}+\sqrt{18}}=\frac{a+b\sqrt{6}}{15}$

⇒ $\frac{(4\sqrt{3}+5\sqrt{2})(4\sqrt{3}-3\sqrt{2})}{(4\sqrt{3}+3\sqrt{2})(4\sqrt{3}-3\sqrt{2})}=\frac{a+b\sqrt{6}}{15}$

⇒$\frac{48-12\sqrt{6}+20\sqrt{6}}{48-18}=\frac{a+b\sqrt{6}}{15}$

⇒ $\frac{18+8\sqrt6}{30}=\frac{a+b\sqrt{6}}{15}$

$\frac{9+4\sqrt6}{15}=\frac{a+b\sqrt{6}}{15}$

we get a=9 and b=4

we have to find the value of x

$(\frac{9}{4})^x(\frac{4}{9})^(2x)=\frac{64}{729}$

⇒ $(\frac{4}{9})^x=(\frac{4}{9})^3$

⇒ x=3

Hence, the value of x is 3