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The sum of the saluares of two
consecutive natural numbers is 113. Find
the numbers
Answers
Answer:
The numbers are 7 and 8.
Step-by-step explanation:
Given:
- Sum of the squares of two consecutive numbers is 113.
To Find:
- The numbers
Solution:
Let us assume the first number as x
Since the numbers are cosecutive,
The second number = x + 1
By given,
Square of first number + Square of second number = 113
Hence,
x² + (x + 1)² = 113
Expanding by using identities,
x² + x² + 2x + 1 = 113
2x² + 2x + 1 = 113
2x² + 2x - 112 = 0
Dividing the whole equation by 2,
x² + x - 56 = 0
Factorizing by splitting the middle term,
x² + 8x - 7x - 56 = 0
x (x + 8) -7 (x + 8) = 0
(x + 8) (x - 7) = 0
Either
x + 8 = 0
x = -8 which is not possible since the number is a natural number
Or
x - 7 = 0
x = 7
Therefore the first number is 7.
The second number = x + 1 = 7 + 1
The second number = 8
Therefore the numbers are 7 and 8.
Verification:
x² + (x + 1)² = 113
7² +(7 + 1)² = 113
49 + 8² = 113
49 + 64 = 113
113 = 113
Hence verified.
Answer:
in this que. 2^3 means 2 power 3
Step-by-step explanation:
let , the two consecutive natural no. =x and x+1
A/Q
x^2 + (x+1)^2 = 113
x^2+ x^2 + 2x + 1 = 113. { ( a+b)^2 = a^2 +2ab + b^2 }
2x^2 +2x +1 - 113 =0
2x^2 + 2x -112 = 0
x^2 +x -56 = 0. {divided by 2 or take commom}
x^2 + (8 - 7)x - 56 =0
x^2 + 8x - 7x - 56 = 0
x ( x +8) -7(x + 8) =0
( x -7 ) (x-8) =0
x - 7 =0 || x -8 =0
x = 7 || x = 8
Thus , if x = 7 and if x = 8
then , x+1 = 8 x+1 = 9
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