Question

The sum of squares of three consecutive even
natural numbers is 200. Find the numbers.
(A) 6,8,10 (B) 8,9, 10
(C) 9,7, 10 (D) 7,8,9​

Answer 1

Answer:

The answer is in the attachment. please refer it. if there are any problems. ask it.

thanks

Answer 2

Answer

Option (A) 6,8,10

Step-by-step explanation:

To find : Three consecutive even numbers

Solution : Let first even number be 'x'

                Then consecutive two even numbers after 'x' will be 'x+2' and 'x+4'

        Sum of squares

             $x^{2} +(x+2)^{2} +(x+4)^{2} = 200$

              $x^{2} +x^{2} + 4x +4+x^{2} +8x+16=200$

              $3x^{2} + 12x + 20 = 200$

              $3x^{2} + 12x - 180 = 0$

       Solving the quadratic equation

              $3x^{2} + 30x - 18x-180 = 0$

              $3x(x+10)-18(x+10)= 0$

       Now x = -10 and x = $\frac{18}{3}$

     Since it is given as natural numbers x= -10 is neglected

     Therefore the three consecutive numbers are 6, 8 , 10.