Question

the sum of two consecutive even numbers is 624.write a second degree equation by taking the first number as x​

Answer 1

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

Given that,

• The sum of two consecutive even numbers is 624.

We know,

• Two consecutive even integers differ by 2.

So, Let assume that

• First integer is x

• Second integer is x + 2

So, According to statement,

$\rm :\longmapsto\: {x}^{2} + {(x + 2)}^{2} = 624$

$\rm :\longmapsto\: {x}^{2} + {x}^{2} + 4 + 4x = 624$

$\rm :\longmapsto\: {2x}^{2} + 4x + 4 = 624$

$\rm :\longmapsto\: {2x}^{2} + 4x + 4 - 624 = 0$

$\rm :\longmapsto\: {2x}^{2} + 4x - 620 = 0$

$\rm :\longmapsto\: 2\bigg[{x}^{2} + 2x - 310\bigg] = 0$

$\red{\rm \implies\:\boxed{ \tt{ \: {x}^{2} + 2x - 310 = 0 \: }}}$

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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.