Question

4.the product of two consecutive integers is 306.we need to find
the integers ,write the equation.​

Answer 1

Answer:

Let the two consecutive positive integers be x and (x +1) .

According to the given condition,

$\: \: \: \: \: (x)(x + 1) = 306 \\ \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + x = 306 \\ {x}^{2} + x - 306 = 0$

The equation to find the integers is

${x}^{2} + x - 306 = 0$

By factorization,

we get the equation

$\: \: \: {x}^{2} + 18x - 17x - 306 = 0 \\ x(x + 18) - 17(x + 18) = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: (x + 18)( x - 17) = 0 \\ \: \: x + 18 = 0 \: (or) \: x - 17 = 0 \\ \: \: \: \: \: \: x = - 18 \: (or) \: x = 17$

Here "x" is an positive integer, so the value of x is 17.

One number = x = 17

Another number = x+1 = 18

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