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Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1....

Solve `sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.`

Text Solution

Verified by Experts

The correct Answer is:
`x = 4, - 14//5`
`L = sqrt(5x^(2) - 6x + 8) and M= sqrt(5x^(2) - 6x - 7) `. Hence,
`L - M = 1 and L^(2) - M^(2) = 15`
`rArr L + M = 15`
Adding we get
`2L = 16`
or `L^(2) = 64`
`5x^(2) - 6x + 8 = 64`
or `5x^(2) - 6x - 56= 0`
or `(x - 4) (5x + 14) = 0`
or `x = 4, - 14//5`
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