Answers

  • Brainly User
2014-09-22T23:41:39+05:30
5^(4x) - 3x5^(2x+1) - 250 =0

5^(4x) = [5^(2x)]^2,

5^(2x+1) = 5x5^(2x)

So Re-write the given equation:-

[5^(2x)]²  - 3x5x[5^(2x)] - 250 = 0

Put 5^(2x) = a, then above equation becomes:-
a² - 15a - 250 = 0 OR a² - 25a + 10a - 250 =0 OR a(a-25) + 10(a-25) 
= (a-25)(a+10)
Now as a = 5^(2x), re-write above equation as:-

[5^(2x) - 25](a+10) = [(5^x)² - 5²][5^(2x)+10] because 5^(2x) = (5^x)².

                           = (5^x + 5)(5^x - 5)[(5^(2x) + 10]

 
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