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CBSE Class 9 Answered

Given that 4^(x+1) + 4^x  = 3^(y+4) - 3^y, where x and y are non-negative integers, then find
the value of x-y.
Asked by a.behera67 | 25 Jan, 2016, 07:59: PM
answered-by-expert Expert Answer
4 to the power of left parenthesis straight x plus 1 right parenthesis end exponent plus 4 to the power of straight x equals 3 to the power of left parenthesis straight y plus 4 right parenthesis end exponent minus 3 to the power of straight y 4 to the power of straight x cross times 4 to the power of 1 plus 4 to the power of straight x space equals space 3 to the power of straight y cross times 3 to the power of 4 space minus 3 to the power of straight y space 4 to the power of straight x left parenthesis 4 plus 1 right parenthesis space equals space 3 to the power of straight y left parenthesis 3 to the power of 4 space minus 1 right parenthesis space 4 to the power of straight x cross times 5 equals 3 to the power of straight y cross times 80 4 to the power of straight x over 3 to the power of straight y equals 16 equals 16 over 1 equals 4 squared over 3 to the power of 0 therefore straight x space equals space 2 space and space straight y space equals space 0 straight x minus straight y space equals 2 minus 0 space equals 2
Answered by Vijaykumar Wani | 27 Jan, 2016, 11:33: AM

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