1.

Solve the equation `10x-1/x=3` by the method of completing the square.

Answer» We have
`10x-(1)/(x)=3`
`implies" "10x^(2)-1=3x`
`implies" "10x^(2)-3x=1`
`implies" "100x^(2)-30x=10" "["multiplying each side by 10"]`
`implies" "(10x)^(2)-2xx10x xx(3)/(2)+((3)/(2))^(2)=10+((3)/(2))^(2)`
`" "["adding "((3)/(2))^(2)" on both sides"]`
`implies" "(10x-(3)/(2))^(2)=(10+(9)/(4))=(49)/(4)=((7)/(2))^(2)`
`implies" "10x-(3)/(2)=+-(7)/(2)" "["taking square root on both sides"]`
`implies" "10x-(3)/(2)=(7)/(2)" or "10x-(3)/(2)=(-7)/(2)`
`implies" "10x=((7)/(2)+(3)/(2))=(10)/(2)=5" or "10x=((-7)/(2)+(3)/(2))=(-4)/(2)=-2`
`implies" "10x=5" or "10x=-2impliesx(5)/(10)=(1)/(2)" or "x=(-2)/(10)=(-1)/(5).`
Hence, `(1)/(2)` and `(-1)/(5)` are the roots of the given equation.


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