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प्रश्न
Solve for x: `1/(x + 4) - 1/(x + 7) = 11/30, x ≠ - 4, 7`.
बेरीज
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उत्तर
Given, `1/(x + 4) - 1/(x + 7) = 11/30`
⇒ `(x + 7 - x - 4)/((x + 4)(x + 7)) = 11/30`
⇒ `3/(x^2 + 4x + 7x + 28) = 11/30`
⇒ `3/(x^2 + 11x + 28) = 11/30`
⇒ 11x2 + 121x + 308 = 90
⇒ 11x2 + 121x + 218 = 0
Comparing with ax2 + bx + c = 0, we get
a = 11, b = 121 and c = 218
∴ `x = (-b +- sqrt(b^2 - 4ac))/(2a)`
= `(-121 +- sqrt(14641 - 9592))/22`
⇒ `x = (-121 +- sqrt(5049))/22`
= `(-121 +- 71.06)/22`
⇒ `x = (-121 + 71.06)/22, (-121 - 71.06)/22`
⇒ `x = (-49.94)/22, (-192.06)/22`
⇒ x = – 2.27, – 8.73.
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