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Question
Solve:
(x2 + 5x + 4)(x2 + 5x + 6) = 120
Solution
(x2 + 5x + 4)(x2 + 5x + 6) = 120
Let x2 + 5x = y
Then (y + 4)(y + 6) = 120
`=>` y2 + 6y + 4y + 24 – 120 = 0
`=>` y2 + 10y – 96 = 0
`=>` y2 + 16y – 6y – 96 = 0
`=>` y(y + 16) – 6(y + 16) = 0
`=>` (y + 16)(y – 16) = 0
Then y = –16 or y = 6
`=>` x2 + 5x + 16 = 0 or x2 + 5x – 6 = 0
`=> x = (-5 +- sqrt((5)^2 - 4(1)(16)))/(2(1))` or `x^2 + 6x - x - 6 = 0`
`=> x = (-5 +- sqrt(-39))/2` or `x(x + 6) - 1(x + 6) = 0`
(reject) or (x + 6)(x – 1) = 0
Then x = – 6 and x = 1
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