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प्रश्न
Solve: (x + 2) (x - 5) (x - 6) (x + 1) = 144.
उत्तर
(x + 2) (x - 5) (x - 6) (x + 1) = 144
⇒ (x + 2) (x - 6) (x - 5) (x + 1)= 144
⇒ (x2 - 4x - 12) (x2 - 4x - 5) = 144
Put x2 - 4x = y
Then (y - 12) (y - 5) = 144
⇒ y2 - 17y + 60 - 144 = 0
⇒ y2 - 17y - 84 = 0
⇒ y2 - 21y + 4y - 84 = 0
⇒ y(y - 21) + 4(y -21) = 0
⇒ (y - 21) (y + 4) = 0
⇒ y - 21 = 0 or y + 4 = 0
⇒ y = 21 or y = -4
But x2 - 4x = y
∴ x2 - 4x = 21
⇒ x2 - 4x - 21 = 0
⇒ x2 - 7x + 3x - 21 = 0
⇒ x(x - 7) + 3(x - 7) = 0
⇒ (x - 7) (x +3) = 0
⇒ x - 7 = 0 or x + 3 = 0
⇒ x = 7 or x = -3
or
x2 - 4x = -4
⇒ x2 - 4x + 4 = 0
⇒ (x - 2)2 = 0
⇒ x - 2 = 0
⇒ x = 2
Hence, x = 7, -3 and 2.
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