If x is a non-negative integer such that 7^(x^(1/2) + 24^(x^(1/2)) =

Question

If x is a non-negative integer such that  7^{\sqrt{x}}+ 24^{\sqrt{x}} = 25^{\sqrt{x}} , what is the value of x?

A. 0
B. 1
C. 2
D. 3
E. 4

Mehakj10 · Answer

tried back solving and directly started from 4, the answer is e.

100mitra · Answer

Correct Option E : 4

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Abhishek009 · Answer

For convenience sake I will start with  x = 4  , as  \sqrt{4 = 2}

So,  7^{\sqrt{4}}+ 24^{\sqrt{4}} = 25^{\sqrt{4}}

Or,  7^2+ 24^2 = 25^2

Or,  49+ 576 = 625  { There is no need to calculate 24^2 as units digit rule 4^2 = 6 will work wonder here.....}

xx9 + xx6 = 625

Hence, answer must be (E) 4

rahulkhannad · Answer

Is there any other approach other than substituting values for x?

Krunaal · Answer

If you can memorize some pythagorean triplets such as,

(3,4,5); (5,12,13); (7,24,25); (8,15,17); (9,40,41)

You will easily identify the pattern and deduce that  \sqrt{x} = 2 , therefore  x = 4

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