Question

the sum of natural number and it square it equal the product of first 3 prime number

Answer 1

Step-by-step explanation:

Please refer the attachment

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The sum of natural number and it square is equal to the product of first 3 prime numbers.

Let assume that the required natural number be x.

We know, first three prime numbers are 2, 3, 5.

So, According to given question,

$\rm :\longmapsto\:x + {x}^{2} = 2 \times 3 \times 5$

$\rm :\longmapsto\: {x}^{2} + x = 30$

$\rm :\longmapsto\: {x}^{2} + x - 30 = 0$

$\rm :\longmapsto\: {x}^{2} + 6x - 5x - 30 = 0$

$\rm :\longmapsto\:x(x + 6) - 5(x + 6) = 0$

$\rm :\longmapsto\:(x + 6)(x - 5) = 0$

$\rm \implies\:x = 5 \: \: \: or \: \: \: x = - 6 \: \{rejected \}$

• Hence, Required number is x = 5.

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Basic Concept Used :-

Writing Systems of  Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.