The sum of the square of two consecutive multiples of 7 is 637. Find the multiples.
Answers
SOLUTION:-
Given:
The sum of the square of two consecutive multiples of 7 is 637.
To find:
The multiples.
Explanation:
Let the number be 7x.
•Consecutive multiples of 7 are numbers where the difference between two numbers is 7
Thus,
The other number be 7(x+1).
It is given that sum of the squares of two consecutive multiples of 7 is 637.
According to the question:
=) (7x)² + [7(x+1)]² = 637
=) 49x² + 49(x² + (1)² +2× x×1) =637
=) 49x² + 49(x² +1 + 2x) = 637
=) 49x² + 49x² +49 + 98x= 637
=) 98x² +98x+49=637
=) 98x² +98x +49 -637=0
=) 98x² +98x -588=0
=) x² + x -6 =0
=) x² +3x -2x -6 =0
=) x(x+3) -2(x+3)=0
=) (x+3)(x-2)=0
=) x+3= 0 or x-2=0
=) x= -3 or x= 2
Now,
One number is 7x, 7 ×2 = 14.
Other number is 7(x+1)
=) 7(2+1)
=) 7 (3)
=) 7×3
=) 21
Thus,
The two consecutive multiples of 7 are 14 & 21.
Hope it helps ☺️
Answer:
Step-by-step explanation:
14 and 21 are the mutliplesof 613.