MATH SOLVE

4 months ago

Q:
# The product of two consecutive positive integers is 1332 explain how you can write and solve a quadratic equation to find the value of the larger integer

Accepted Solution

A:

ANSWER:
The product of two consecutive positive integers is 1332. The larger number is 37.
SOLUTION:
Given, the product of two consecutive positive integers is 1332.
Let the larger number be x.
Then the smaller number is x β 1 [as the given numbers are consecutive]Product of the two numbers is 1332 β larger number [tex]\times[/tex] smaller number = 1332
x(x β 1) = 1332
(x)x β (x)(1) = 1332 Β [tex]\begin{array}{l}{x^{2}-x=1332} \\ {x^{2}-x-1332=0}\end{array}[/tex]This is quadratic equation. let us find the x value by factorization method.we need to make the two terms product as such that, difference of both numbers should be equal to 1, as x coefficient is 1.[tex]x^{2}-x-2 \times 666=0[/tex]keep doing this until we get the difference equals to 1.[tex]x^{2}-x-4 \times 333=0[/tex][tex]\mathrm{x}^{2}-\mathrm{x}-12 \times 111=0[/tex][tex]x^{2}-x-36 \times 37=0[/tex]we got difference 1 that is 37 β 36 = 1writing the x coefficient in terms of those numbers (36, 37)[tex]\mathrm{x}^{2}-(37-36) \mathrm{x}-36 \times 37=0[/tex][tex]x^{2}-37 x+36 x-36 \times 37=0[/tex]now, take the common termsx(x β 37) + 36(x β 37) = 0 Β (x β 37)(x + 36) = 0
x β 37 = 0 or x + 36 = 0
x = 37 or -36
we can neglect -36, because given numbers are positive numbers.Hence, the larger number is 37