1.

If `abx^(2)=(a-b)^(2)(x+1)`, then find the value of `1+(4)/(x)+(4)/(x^(2))` in terms of a and b.

Answer» Since `abx=(a-b)^(2)(x+1)`
`implies (x+1)/(x^(2))=(ab)/((a-b)^(2)) implies (1)/(x)+(1)/(x^(2))=(Ab)/((a-b)^(2))`
`implies (4)/(x)+(4)/(x^(2))=(4ab)/((a-b)^(2))`
`implies 1+(4)/(x)+(4)/(x^(2))=1+(4ab)/((a-b)^(2))`
`=(a^(2)+b^(2)-2ab+4ab)/((a-b)^(2))=(a^(2)+b^(2)+2ab)/((a-b)^(2))=((a+b)^(2))/((a-b)^(2))`


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