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Question
Solve :
`2x - 3 = sqrt(2x^2 - 2x + 21)`
Solution
Given : `2x - 3 = sqrt(2x^2 - 2x + 21)`
by squaring on both side
`(2x - 3)^2 = 2x^2 - 2x + 21`
`(2x)^2 + (3)^2 - (2) (2x) (3) = 2x^2 - 2x + 21`
`4x^2 + 9 - 12x = 2x^2 - 2x + 21`
`2x^2 = 10x + 12`
`2x^2 - 10x - 12 = 0`
by splitting the mid term
`2x^2 - 12x + 2x - 12 = 0`
`2x (x - 6) + (x - 6) = 0`
`(2x + 2) (x - 6) = 0`
here the values of x are
2x + 2 = 0
x = -1
x - 6 = 0
x = 6
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