Math, asked by prajwal8934, 11 months ago

of the squares of two consecutive even positive integers
Sed by 100, then it will be 10 times the difference of their
33) If the sum of the squar
is increased by 100, then;
squares, find the integers.

Answers

Answered by amitnrw
2

numbers are 2 , 4     or  16 , 18

Step-by-step explanation:

Question is :

If the sum of the squares of two consecutive even positive integer is increased by 100 then it will be 10 times the difference of their square find the integer​

Two consecutive even integers

2n  & 2(n + 1)

Sum of squares = (2n)² + (2(n+1))²

= 4( n² + n² + 1 + 2n)

= 4(2n² + 2n + 1)

increased by 100

4(2n² + 2n + 1) + 100

= 4(2n² + 2n + 1) + 4*25

= 4(2n² + 2n + 26)

Difference of squares

(2(n+1))² - (2n)²

= 4(n² + 1 + 2n - n²)

= 4(2n + 1)

4(2n² + 2n + 26)  = 10 *  4(2n + 1)

=> 2n² + 2n + 26 = 20n + 10

=>2n² - 18n + 16 = 0

=> n² - 9n  + 8= 0

=> n² - 8n - n + 8 = 0

=> (n - 1)(n - 8) = 0

=> n = 1 , 8

numbers are

2 , 4     or  16 , 18

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