Find a natural number whose square diminished | vedclass

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

Question

(D) Let $n$ be the required natural number.According to the problem,the square of the number diminished by $84$ is $n^2 - 84$.The expression for thric

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) Let $n$ be the required natural number.According to the problem,the square of the number diminished by $84$ is $n^2 - 84$.The expression for thrice of $8$ more than the number is $3(n + 8)$.Setting these equal,we get the quadratic equation:$n^2 - 84 = 3(n + 8)$$n^2 - 84 = 3n + 24$$n^2 - 3n - 108 = 0$To solve this,we factor the quadratic equation:$n^2 - 12n + 9n - 108 = 0$$n(n - 12) + 9(n - 12) = 0$$(n - 12)(n + 9) = 0$This gives $n = 12$ or $n = -9$.Since $n$ must be a natural number,we discard $n = -9$.Therefore,the required natural number is $12$.

Find a natural number whose square diminished by $84$ is equal to thrice of $8$ more than the given number.

Similar Questions

State whether the quadratic equation $x^{2}-3x+4=0$ has two distinct real roots. Justify your answer.

Find the discriminant of the following quadratic equation: $5x^{2} - 4\sqrt{2}x - 1 = 0$.

$x=2$ is a solution of the equation $\ldots \ldots \ldots \ldots.$

Which of the following polynomials does not have any real zero?

If the roots of the quadratic equation $5x(2x - 3) - 4 = 0$ exist,find them using the method of completing the square.

Vedclass Test Series

Exam Paper Generator

Online Exam Module