IIT JEE , AIEEE Forum - Mathematics , Algebra - plz solve this , the no.of real solutions of

sourab_MCA

2^(x/2)+(

2+1)^x=(5+2

2)^(x/2)

Pavis

x=0 nd x=2 are the two solutions

sourab_MCA

nice GUESS, but unfortunately its wrong.
LOL

Pavis

sorry x=0 is not the solution only x =2

nadeemoidu

EDIT: there was an error in the previous answer . Now i think it is right. sorry for the mistake.

$2^{ rac{x}{2}} + (sqrt{2} + 1)^x =(5 + 2 sqrt{2})^{ rac{x}{2}}$

=> $(\sqrt2)^x + (\sqrt{2} + 1)^x =[(\sqrt2)^2+(\sqrt{2} + 1)^2]^{\frac{x}{2}}$

Obviously , x=2 is a solution.

Now, this is of the form, $a^{\frac{x}{2}} + b^{\frac{x}{2}} =(a + b)^{\frac{x}{2}}$

It can be proved that this does not have any other solution by using inequalities.

So x=2 is the only solution.

sourab_MCA

it is true that there is only one solution , but x=2 is the solution(not x=1),
but i dont know how to solve this.

nadeemoidu

Check the answer now . sorry for the earlier wrong answer.

sourab_MCA

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