A natural number,when increased by 12,equals | vedclass

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Question

(A) Let the natural number be $x$.According to the question,$x + 12 = \frac{160}{x}$On multiplying both sides by $x$,we get:$x^2 + 12x = 160$$x^2 + 12

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) Let the natural number be $x$.According to the question,$x + 12 = \frac{160}{x}$On multiplying both sides by $x$,we get:$x^2 + 12x = 160$$x^2 + 12x - 160 = 0$Now,factorizing the quadratic equation:$x^2 + 20x - 8x - 160 = 0$$x(x + 20) - 8(x + 20) = 0$$(x + 20)(x - 8) = 0$This gives two possible values for $x$:$x = -20$ or $x = 8$.Since the question specifies a natural number,$x$ must be positive.Therefore,$x = 8$ is the required natural number.

$A$ natural number,when increased by $12$,equals $160$ times its reciprocal. Find the number.

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