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23basu3
16.07.2019 •
Mathematics
15 points plz let k be constant. if the equation (x+2)(x+3) = kx +2 has equal positive roots,then x=?
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Ответ:
To complete the square on the left we add ((5-k)/2)² to each side:
(x+(5-k)/2)²=((5-k)/2)²-4.
Take a look at the right hand side: when this is zero we have equal roots:
((5-k)/2)²=4, (5-k)/2=±2, 5-k=±4, k=5∓4, giving us k=1 or 9.
(5-k)/2 is 2 or -2. So if k=9, (x-2)²=0. And x=2 is the positive root.
Ответ:
That would be the right answer.