Question

Find two consecutive positive even numbers

the sum of whose squares is 20. Separate
the two numbers with a comma.

Answer 1

-4,2

Explanation:

`let \: two \: consecutive \: even \: numbers \: be \: x \: and \: x + 2 \\ so \: by \: the \: question \\ {x}^(2) + {(x + 2)}^(2) = 20 \\ or \: {x}^(2) + {x}^(2) + 4x + 4 = 20 \\ or \: 2 {x}^(2) + 4x = 20 - 4 \\ or \: 2( {x}^(2) + 2x) = 16 \\ or {x}^(2) + 2x = 8 \\ or \: {x}^(2) + 2x - 8 = 0 \\ or \: {x}^(2) + (4 - 2)x - 8 = 0 \\ or \: {x}^(2) + 4x - 2x - 8 = 0 \\ or \: x(x + 4) - 2(x + 4) = 0 \\ or \: (x + 4)(x - 2) = 0 \\ either \: x + 4 = 0 \\ or \: x = - 4 \\ or \: x - 2 = 0 \\ orx = 2`

therefore, x= -4 and 2