Question

Page
* Find value of x, y
(32)^x ÷2^y+1=1,16^4-x/2 -8^y=0
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Answer 1

Answer:

Notice that y≥0, y≠1 and x≠0. If (x,y) is a solution then (−x,y) is a solution too. Hence W.L.O.G x>0.

It seems that x and y cannot be too far from each other, otherwise LHS would become larger than RHS. We'll find out this. Suppose that z=|x−y|. Notice that z≠0. Now, we have

z2(x+y)2=|x−y|2(x+y)2=(x2−y2)2=16y+1

And since y≥0, y≠1 and x>0, then

z2=16y+1(x+y)2<4(1+y)2(1+y)2=4 ⟹ z<2

Therefore z=1. It follows that x=y±1 and equation turns into a simple quadratic for y.

Step-by-step explanation:

I hope this helps u