Question

pls answer this question

Answer 1

6^2 + 8^2 = 36+64 = 100. So the two consecutive numbers are -8 and -6 or 6 and 8.

Hope it helps you

Answer 2

QUESTION

The sum of the squares of two consecutive even natural numbers is 100. Find the numbers.

ANSWER

Let the two consecutive even natural numbers be x and x +2.

As per the given condition.

$\bold{x^2 + (x + 2)^2 = 100}$

$\implies\bold{ x^2 + x^2 + 4x + 4 = 100}$

$\bold{\implies 2x^2 + 4x + 4 – 100 = 0}$

$\bold{\implies 2x^2 + 4x – 96 = 0}$

Dividing by 2 we get,

$x^2 + 2x – 48 = 0$

$\bold{\implies x^2 – 6x + 8x – 48 = 0}$

$\bold{\implies x (x – 6) + 8 (x – 6) = 0}$

$\bold{\implies (x – 6) (x + 8) = 0}$

$\bold{\implies x – 6 = 0 \:or\: x + 8 = 0}$

$\bold{\implies x = 6 \:or \:x = – 8}$

x is an natural number

$\bold{∴ x \:cannot \:be \: – 8}$

∴ x = 6

And x + 2 = 6 + 2 = 8

∴ The two consecutive even natural numbers are 6 and 8 respectively.