Question

two consecutive numbers in which the sum of 3 times the first number and the square of second number is 85.find the number​

Answer 1

from the quadratic equation:

x+12=0

x=-12

x-7=0

x=7

Answer 2

Two consecutive numbers are (-12 and -11) or ( 7 and 8)

Step-by-step explanation:

• Given that

        First number = X

        Second number = X +1

• Here it is given that the sum of 3 times the first number and the square of second number is 85. Means

      3×First number + (second number)² =85

• 3×X + (X +1)² =85

        3X + X² + 2X + 1 =85

        X² + 5X + 1 =85

        X² + 5X + 1 - 85 =0

        X² + 5X - 84 =0

• By middle term splitting method

        X² + 12X -7X - 84 =0

        X( X+12) -7(X +12) =0

        (X+12 ) (X -7) = 0

• So

        X + 12 = 0        or        X - 7 = 0

        X = -12             or         X = 7

• If  X = -12

        First number = X = -12

        Second number = X +1 = -12 +1 = -11

• If  X = 7

         First number = X = 7

         Second number = X +1 = 7 +1 = 8