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Find the range of maximum value M of 3^x + 5^x – 9^x – 25^x +15^x 0 5 3 9

Find the range of maximum value M of 
3^x + 5^x – 9^x – 25^x +15^x
  1. 0
  2. 5
  3. 3
  4. 9

Grade:12

2 Answers

mycroft holmes
272 Points
6 years ago
Let 3x = a, and 5x = b. Let the given expression be S. We look at -S.
 
Now -2S+2 = 2(a2+b2-ab-a-b)+2 = (a-1)2+(b-1)2+(a-b)>=0.
 
Hence Sx = 5= 1 i.e. when x = 0.
mycroft holmes
272 Points
6 years ago
Small error, we have S
 
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