Question

1 added to the product of two consecutive even numbers gives 289.from a second degree equation to solve the problem​

Answer 1

Answer:

So, 1 + (x * y) = 289, where y = x + 2

1 + (x * (x +2) = 289

x * (x +2) = 288

x^2 + 2x = 288

x^2 + 2x - 288 = 0

Solving that quadratic equation, the two consecutive numbers are 16 and 18. or -16 and -18

Answer 2

⇒  Let two consecutive even number be xand x+2.

According to the question,

⇒  x2+(x+2)2=340

⇒  x2+x2+4x+4=340

⇒  2x2+4x+4=340

⇒  2x2+4x+4−340=0

⇒  2x2+4x−336=0

⇒  x2+2x−168=0

⇒  x2+14x−12x−168=0

⇒  x(x+14)−12(x+14)=0

⇒  (x+14)(x−12)=0

⇒  x+14=0 and x−12=0

⇒  x=−14 and x=12

∴  One number is 12

⇒  Other number =12+2=14

⇒  Required product =12×14=168