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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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.

Similar Questions

The speed of a motor-boat in still water is $x \, km/hr$ and the speed of the current of the river is $5 \, km/hr$. Given $x$ > 5, what is the time taken to cover a distance of $y \, km$ upstream?

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-3}+\frac{x-3}{x+1}=\frac{5}{2}$

In quadratic equation $ax^{2} + bx + c = 0$,where $a \neq 0$,$b = 0$,and $D > 0$,then both the roots of the equation are .....

$120$ kites were divided equally among a certain number of children in a school. If there were $4$ children fewer,each child would have received $1$ kite more. Find the number of children.

Solve the following quadratic equation using the method of factorization: $3x^{2} = -11x - 10$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module