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Question
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Solution
Substituting x = 3 in the given eqution
L.H.S. = `sqrt((3)^2 - 4 xx 3 + 3) + sqrt((3)^2 - 9)`
= `sqrt(9 - 12 + 3) + sqrt(9 - 9)`
= 0 + 0
= 0
R.H.S. = `sqrt(4(3)^2 - 14 xx 3 + 16)`
= `sqrt(36 - 42 + 16)`
= `sqrt(52 - 42)`
= `sqrt(10)`
Since, L.H.S. ≠ R.H.S.
Therefore, x = 3 is not a root of the given equation.
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