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Question

Find the value of x and yfor the equations a2xb2y=0;a2bx+b2ay=a+b where x,y0.

A
x=a2,y=b2
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B
x=b2,y=a2
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C
x=ba,y=ab
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D
x=1b,y=1a
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Solution

The correct option is A x=a2,y=b2
a2xb2y=0(Given)
ya2xb2=0.....(1)
a2bx+b2ay=a+b(Given)
a2by+b2ax=(a+b)xy.....(2)
Multiplying eqN(1) by a, we get
a3yb2ax=0.....(3)
Adding eqn(2)&(3), we have
(a2by+b2ax)+(a3yb2ax)=(a+b)xy
a2by+b2ax+a3yb2ax=(a+b)xy
a2y(b+a)=(a+b)xy
x=a2
Substituting the value of x in eqn(1), we have
ya2a2b2=0
y=b2
Hence the value of x and y are a2 and b2 respectively.
Hence the correct answer is (A)x=a2,y=b2.

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