Find a natural number whose square diminished | vedclass

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(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

$12$

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(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.

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