IF : $$\LARGE{(\sqrt{2})^x+(\sqrt{3})^x=(\sqrt{13}^{\frac{x}{2}})}$$

then the number of values of x = ?

Question

IF : $$\LARGE{(\sqrt{2})^x+(\sqrt{3})^x=(\sqrt{13}^{\frac{x}{2}})}$$ 

then the number of values of x = ?

experimentx · Answer

what's the ... on the left??

mathslover · Answer

what's the?? 

I didn't get you @experimentX

experimentx · Answer

(13)^(x/4) ??

mathslover · Answer

Yes ... 
$$\large{2^{\frac{x}{2}}+3^{\frac{x}{2}}=13^{\frac{x}{4}}}$$

anonymous · Answer

is this correct ?

$$\large \sqrt{13}^{\frac{x}{2}}=13^{\frac{x}{4}}=(9+4)^{\frac{x}{4}} \ge 3^{\frac{x}{2}}+2^{\frac{x}{2}} $$

and looking for the condition for which equality occurs...maybe using binomial theorem

mathslover · Answer

May be or may not be .. 

But the book is showing the answer as 1 ... 

can u explain more? 

why dont u check it out by checking the answer that you got with the book's ans.

mathslover · Answer

@mukushla any hint?

anonymous · Answer

im workin on it...

mathslover · Answer

take ur time then

anonymous · Answer

will this help?|dw:1343486804285:dw|