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Daca a la puterea a 2 - b la puterea a 2 = 24 si 3a+3b = 6 atunci a-b = .......


Răspuns :

[tex]a^2-b^2=24 \Leftrightarrow (a+b)(a-b)=24 \; \; (1) \\ 3a+3b=6 \Leftrightarrow 3(a+b)=6 \Rightarrow a+b=2 \; \; (2) \\ (2) \rightarrow (1) \Rightarrow a-b=\dfrac{24}{2}=12 [/tex]
a²-b²=24
3a+3b=6|:3 <=>a+b=2=>a=2-b
inlocuim a cu 2-b in prima ecuatie
(2-b)²-b²=24
folosim formula (a-b)²=a²-2ab+b²
4-4b+b²-b²=24
(+b² se reduce cu -b²)
<=> 4-4b=24
-4b=20=> b= -5
a+b=2
a-5=2=>a=7
a-b=7-(-5)= 7 + 5=12