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प्रश्न
Solve: (x – 5)(x – 7) (x + 6)(x + 4) = 504
उत्तर
(x – 5)(x + 4)(x – 7)(x + 6) = 504
(x2 – x – 20)(x2 – x – 42) = 504
Let y = (x2 – x)
(y – 20)(y – 42) = 504
⇒ y2 – 42y – 20y + 840 = 504
⇒ y2 – 62y + 336 = 0
⇒ (y – 56)(y – 6) = 0
⇒ (y – 56) = 0 or (y – 6) = 0
⇒ x2 – x – 56 = 0 or x2 – x – 6 = 0
⇒ (x – 8)(x + 7) = 0 or (x – 3)(x + 2) = 0
⇒ x = 8, – 7 or x = 3, – 2
The roots are 8, – 7, 3, – 2
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