Question

What is the answerofthis theproduct of two consecutive positive integers is 306 we need tofind integers?

Answer 1

Answer:

Let the numbers be x and x + 1

So the product of these two numbers is 306. Writing it in equational form we get,

=> ( x ) ( x + 1 ) = 306

=> x² + x = 306

=> x² + x - 306 = 0

=> x² + 18x - 17x - 306 = 0

=> x ( x + 18 ) -17 ( x + 18 ) = 0

=> ( x + 18 ) ( x - 17 ) = 0

=> x = 17, -18.

Since it is mentioned x is a positive integer, we neglect -18.

Hence the value of x is 17.

Hence the other integer is x + 1 = 17 + 1 = 18.

Hence the two integers are: 17 and 18

Answer 2

$\mathsf{\huge{\underline{Question:-}}}$

What is the answer of this the product of two consecutive positive integers is 306

$\mathtt{\huge{Solution:-}}$

Revise some memories;

What is Consecutive Number?

=> If x is any number, then x and x + 1 are consecutive numbers.

$\mathfrak{\bold{Solution:-}}$

Let to be Required Consecutive Positive Number x and x+1

Product of consecutive Number means multiplication of Numbers.

=> (x)(x+1)

Here,

Product of Consecutive Positive Number=)306 (Given).

$\mathbb{ACCORDING TO THE QUESTION; }$

(x)(x+1)=306

x²+x=306

x²+x-306=0

$\mathbb{SOLVING BY FACTORIZATION METHOD!!!}$

x²+x-306=0

x²+18x-17x-306

x(x+18)-17(x+18)

(x+18)(x-17)=0

Solution:- x-17=0

hence, x=17

_________________
Solution:- (x+18)=0

Hence, x=-18
(Removed Because it is in the form of negative)
_________________

Again, According to the Question

Integers are (x) and (x+1) -----(Equation @)

Substitute the value of x in Equation @

x=17

And,

x+1=) 17+1=18

___________________
$\mathtt{Conclusion:- 17 and 18 are Required Integers .}$
____________________


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