Question

the sum of a number and it's square is 90 then the two numbers​

Answer 1

☆ Concept :-

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Here we have been provided that there is a number, suppose, x, the sum of this number and its square is 90. So, if we interpret this information then we will conclude with a quadratic equation, which can be solved by the help of factorization.

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☆ Given Information :-

• The sum of a number and its square is 90.

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☆ To Find :-

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• The number

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☆ Solution :-

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Let us assume the number to be x, therefore, according to the question,

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→ x² + x = 90

→ x² + x - 90 = 0

We conclude with this equation, which is a quadratic equation. Now, we will solve it,

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$\sf \longrightarrow {x}^{2} + x - 90 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \longrightarrow {n}^{2} + 10n - 9n - 90 = 0 \: \: \: \: \\ \\ \sf \longrightarrow n(n + 10) - 9(n + 10) = 0 \\ \\ \sf \longrightarrow (n + 10)(n - 9) = 0 \: \: \: \: \: \: \: \: \: \:$

Now, we have :-

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$\sf \longrightarrow \sf \begin{cases} \sf 1. (n + 10) = 0 = n = - 10 \\ \\ \sf2 .(n - 9) = 0 = n = + \: 9\end{cases}$

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We know that, since its a positive integer, it can't be negative. Thus, the required number is 9.

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