If 2 power 'x'+3 power 'y'=17 and 3(2)power 'x'-2(3) power 'y'=6,then x and y =
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Answer:
Answer below
Step-by-step explanation:
2^x + 3^y = 17 and 2^(x+2) + 3^(y+1) = 5
Expanding the second, we get, 4(2^x) + 3(3^y) = 5
Let 2^x = a and 3^y = b;
==> a + b = 17 ..... (1)
and 4a + 3b = 5 .... (2)
Solving the two equations (1) and (2), a = -46 and b = 63
==> 2^x = -46; which is not possible; since power of 2 with any real number can never be negative. Hence, I suppose the question is WRONG or a typographic error has occured in presenting the question.
However, let me consider the second part as, 2^(x+2) - 3^(y+1) = 5
Proceeding in the above lines, it is, 4a - 3b = 5and the
other one is a + b = 17.
Solving these two equations, we get a = 3 and b = 9
a = 8; ==> 2^x = 8
==> 2^x = 2^3
As base on both sides are same, x = 3
Similarly proceeding, 3^y = 9; ==> 3^y = 3^2; ==> y = 2
Thus the solutions are: (x, y) = (3, 2)
Answer:
answer for the given problem is given
