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प्रश्न
Solve: (x – 4)(x – 2)(x- 7)(x + 1) = 16
उत्तर
(x – 4)(x – 7) (x – 2)(x + 1) = 16
⇒ (x – 4)(x – 2)(x – 7)(x + 1) = 16
⇒ (x2 – 6x + 8)(x2 – 6x – 7) = 16
Let x2 – 6x = y
(y + 8)(y – 7) = 16
⇒ y2 – 7y + 8y – 56 – 16 = 0
⇒ y2 + y – 72 = 0
⇒ (y + 9)(y – 8) = 0
y + 9 = 0
x2 – 6x + 9 = 0
(x – 3)2 = 0
x = 3, 3
or
y – 8 = 0
x2 – 6x – 8 = 0
x = `(6 +- sqrt(36 - 4(1)(- 8)))/(2(1))`
= `(6 +- sqrt(36 + 32))/2`
= `(6 + sqrt(68))/2`
= `(6 +- 2sqrt(17))/2`
= `2 ((3 +- sqrt(17)))/2`
= `3 + sqrt(17)`
Roots are `3, 3, 3 +- sqrt(17)`
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