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Daca media aritmetica a numerelor 5 si x este egala cu media lor geometrica,atunci x este...

Răspuns :

Ma=(5+x)/2
Mg=√(5*x)
(5+x)/2=√5x
Ridici la patrat si ai
x²+10x+25=20x
x²-10x+25=0 - ecuatie de gradul doi
Δ=b²-4ac=100-100=0 deci ecuatia are o singura solutie deci
x=-b/2a=10/2=5
(5+x)/2=√5x
(25+10x+x²)/4=5x
25+10x+x²=20x
x²-10x+25=0
(x-5)²=0
x-5=0
x=5