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Question

Given p=3^i+2^j+4^k,a=^i+^j,b=^j+^k,c=^i+^k and P=xa+yb+zc, then x,y,z are respectively.

A
32,12,52
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B
12,32,52
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C
52,32,12
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D
12,52,32
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Solution

The correct option is B 12,32,52
p=xa+yb+zc
3^i+2^j+4^k=x(^i+^j)+y(^j+^k)+z(^i+^k)
3^i+2^j+4^k=(x+z)^i+(x+y)^j+(y+z)^k
On comparing both sides the coefficients of ^i,^j,^k, we get
x+z=3 ...........(i)
x+y=2 ...........(ii)
and y+z=4 ...........(iii)
On solving Eqs. (i),(ii) and (iii), we get
X=12,y=32,z=52

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