The sum of the squares of two consecutive numbers is 313.
Answers
Answer:
square both and add together to equal 313b.Since the number are denfined to be natural,x= - 13 is not a solution . Therefore,,and.The two numbers are 12and13
Answer:
-13 and -12 (or) 12 and 13
Step-by-step explanation:
Given :
The sum of the squares of two consecutive numbers is 313.
To find :
the numbers
Solution :
Let the two consecutive numbers be x and (x + 1)
Square of x = x²
Square of (x + 1) = (x + 1)²
x² + (x + 1)² = 313
x² + [ x² + 1² + 2(x)(1) = 313
x² + x² + 1 + 2x = 313
2x² + 1 + 2x = 313
2x² + 2x + 1 = 313
2x² + 2x = 313 - 1
2x² + 2x = 312
2x² + 2x - 312 = 0
Taking 2 as common,
2 [ x² + x - 156 ] = 0
x² + x - 156 = 0/2
x² + x - 156 = 0
Now, factorize by splitting middle term.
x² + 13x - 12x - 156 = 0
x(x + 13) - 12(x + 13) = 0
(x + 13) (x - 12) = 0
⇒ x = -13, 12
If x = -13,
the two consecutive numbers are -13 and -12.
If x = 12,
the two consecutive numbers are 12 and 13.
Note : If the two consecutive numbers must be natural numbers, then answer is 12 and 13.