1.

Solve the following quadratic equation : `10x-(1)/(x)=3`

Answer» Given equation is
`10x-(1)/(x)=3`
`implies10x^(2)-1=3x`
`implies10x^(2)-3x-1=0`
`implies10x^(2)-(5-2)x-1=0`
`implies10x^(2)-5x+2x-1=0`
`implies5x(2x-1)+1(2x-1)=0`
`implies(5x+1)(2x-1)=0`
`implies5x+1=0or2x-1=0`
when `5x+1=0impliesx=-(1)/(5)`
and `2x-1=0impliesx=(1)/(2)`
Hence, `-(1)/(5)and(1)/(2)` are roots of the equation.


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