1.

Solved the following equation by the method of completing the square : 4sqrt3x^(2)+5x-2sqrt3=0

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Solution :We have, `4sqrt3x^(2)+5x-2SQRT3=0`
Dividing each term by `4sqrt3` we, get
`x^(2)+(5)/(4sqrt3)x=(2sqrt3)/(4sqrt3)=0`
`impliesx^(2)+(5)/(4sqrt3)x=(1)/(2)`
Adding `((1)/(2)"coefficient of x")^(2)i.e.,((5)/(8sqrt3))^(2)` to both SIDES, we get
`x^(2)+(5)/(4sqrt3)x+((5)/(8sqrt(3)))^(2)=((5)/(8sqrt3))^(2)+(1)/(2)`
`implies(x+(5)/(8sqrt3))^(2)=(25)/(192)+(1)/(2)`
`implies(x+(5)/(8sqrt3))^(2)=(25+96)/(192)`
`implies(x+(5)/(8sqrt3))^(2)=(121)/(192)`
Taking square root of both sides, we get
`x+(5)/(8sqrt3)=+-(11)/(8sqrt3)`
`:.x=-(5)/(8sqrt3)+-(11)/(8sqrt3)=(-5+-11)/(8sqrt3)`
`impliesx=(-5+11)/(8sqrt3)orx=(-5-11)/(8sqrt3)`
`impliesx=(3)/(4sqrt3)orx=(-2)/(sqrt3)`
Hence, `x=(3)/(4sqrt3)orx=(-2)/sqrt3)` are the solutions of given equation.


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