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Question

Question 9 (vi)
Solve the following pair of equations
xa+yb=a+b, xa2+yb2=2,where a,b 0

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Solution

Given pair of linear equations is:
xa+yb=a+b...(i), xa2+yb2=2...(ii),where a,b 0
Dividing the first equation by 'a' on both sides and subtracting it from the second equation, we get
First equation:xa2+yab=1+ba, Subtracting,we get, y(1b21ab)=21bay(abab2)=21bay(abab2)=1bay(abab2)=abay=ab2ay=b2
Now, put the value of y in Eq. (ii), we get
xa2+b2b2=2 xa2=21=1 xa2=1 x=a2
Hence, the required values of x and y are a2 and b2, respectively.

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