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in Quadratic Equations by (46.2k points)
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Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is : 

(a) 4 

(b) 5 

(c) 6 

(d) 10

1 Answer

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by (49.2k points)
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Best answer

(b) 5

Let the natural number be x. Then,

3x2 - 4x = 50 + x

⇒ 3x2 - 4x = 50 + 0

⇒ 3x2 - 15x + 10x - 50 = 0

⇒ 3x(x - 5) + 10(x - 5) = 0

⇒ (3x + 10 )(x - 5) = 0

⇒ x = \(-\frac{10}{3},5\) 

Rejecting x = \(-\frac{10}{3}\) (not a natural number), 

x = 5.

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