Answer:
The Two Consecutive integers are 7 and 8.
Step-by-step explanation:
Let the first Integer be x
Since the two numbers are consecutive
therefore the second number will be x+1
Now given:
the square of the second integer added to 3 times the first is equal to 85
Hence framing the above sentence in mathematical form we get;
[tex](x+1)^2+3x=85[/tex]
Now Solving the above equation we get;
since [tex](a+b)^2 = a^2+2ab+b^2[/tex]
[tex]x^2+2x+1+3x=85[/tex]
Using addition property we get;
[tex]x^2+5x+1-85=0[/tex]
Using Subtraction property we get;
[tex]x^2+5x-84=0[/tex]
Now factorizing above equation we get;
[tex]x^2+12x-7x-84=0\\x(x+12)-7(x+12)=0\\(x-7)(x+12)=0\\x-7=0 \ \ \ \ \ \ \ \ or \ \ \ \ \ \ x+12 = 0\\x= 7\ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ \ x=-12[/tex]
Now we get 2 values of x which is 7 and -12.
Since it is given that number is positive Integer hence the number will be 7
and the other number would 7 + 1 = 8.
