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Solution for Solve : (X² + 5x + 4)(X² + 5x + 6) = 120 - ICSE Class 10 - Mathematics

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Question

Solve : (x² + 5x + 4)(x² + 5x + 6) = 120

Solution

(x² + 5x + 4)(x² + 5x + 6) = 120

Let `x^2 + 5x = y`

then (y + 4)(y + 6) = 120

`=> y^2 + 6y + 4y + 24 - 120 = 0` 

`=> y^2 + 10y - 96 = 0`

`=> y^2 + 16y - 6y - 96 = 0`

`=> y(y + 16) - 6(y + 16) = 0`

=> (y + 16) (y - 16) = 0

then y = -16 or y = 6

`=> x^2 + 5x + 16 = 0 or x^2 +  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

`=> 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

  Is there an error in this question or solution?
Solution Solve : (X² + 5x + 4)(X² + 5x + 6) = 120 Concept: Quadratic Equations.
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