If 72x . 48y = 6xy, where x and y are nonzero rational numbers, then x + y equals
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Hello friend,
72^x ∙ 48^y = 6^xy
We have to solve indexes in this problem
(2×2×2×3×3)^x ∙ (2×2×2×2×3)^y = 6^xy
3^(2x+y).2^(3x+4y) = 2^xy.3^xy
Comparing indexes,
2x+y = xy …..(i)
3x + 4y = xy …..(ii)
From (i) & (ii)
2x+y=3x+4y
x = – 3y
Putting x = – 3y in (i)
2(-3y) + y = (-3y.y)
–5y = – 3y^2
y=5/3
But x=-3y
x = -3(5/3)
x = -5
x+y = -5 + 5/3
x+y = -10/3
Hence value of x+y = -10/3
Hope that was useful...
72^x ∙ 48^y = 6^xy
We have to solve indexes in this problem
(2×2×2×3×3)^x ∙ (2×2×2×2×3)^y = 6^xy
3^(2x+y).2^(3x+4y) = 2^xy.3^xy
Comparing indexes,
2x+y = xy …..(i)
3x + 4y = xy …..(ii)
From (i) & (ii)
2x+y=3x+4y
x = – 3y
Putting x = – 3y in (i)
2(-3y) + y = (-3y.y)
–5y = – 3y^2
y=5/3
But x=-3y
x = -3(5/3)
x = -5
x+y = -5 + 5/3
x+y = -10/3
Hence value of x+y = -10/3
Hope that was useful...
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