Find two consecutive positive even numbers the sum of whose squares is 20. Separate the two numbers with a comma.

Question

Find two consecutive positive even numbers
the sum of whose squares is 20. Separate
the two numbers with a comma.

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Josie 2 days 2021-10-11T20:40:51+00:00 1 Answer 0

Answers ( )

    0
    2021-10-11T20:42:21+00:00

    Answer:

    -4,2

    Step-by-step 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

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