Răspuns :
Răspuns: [tex]\bf \overline{ab}\in\{14,48\}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\bf \overline{ab}= ??[/tex]
[tex]\bf a,b- cifre[/tex]
[tex]\bf a,b\in\{0,1,2,3,4,5,6,7,8,9\}[/tex]
[tex]\bf a\neq 0[/tex]
[tex]\bf \sqrt{a} =\dfrac{b}{4}[/tex]
[tex]\bf \text{\bf Daca \underline{a = 1}}\implies \sqrt{1^{2} } =1[/tex]
[tex]\bf \text{\bf Daca \underline{a = 4}}\implies\sqrt{4} = \sqrt{2^{2} } = 2[/tex]
[tex]\bf \text{\bf Daca \underline{a = 9}}\implies\sqrt{9} = \sqrt{3^{2} } = 3[/tex] ⇒ [tex]\bf \sqrt{a} \in \{1,4,9\}[/tex]
Analizam fiecare caz in funcție de ce valoare poate avea a
[tex]\bf \text{\bf Daca \underline{a = 1}}\implies \sqrt{1} =\dfrac{b}{4} \implies 1=\dfrac{b}{4} \implies \underline{b=4}[/tex]
[tex]\bf \text{\bf Daca \underline{a = 4}}\implies \sqrt{4} =\dfrac{b}{4} \implies 2 =\dfrac{b}{4} \implies \underline{b=8}[/tex]
[tex]\bf \text{\bf Daca \underline{a = 9}}\implies \sqrt{9}=\dfrac{b}{4} \implies 3 =\dfrac{b}{4} \implies b=12 \:\:\: \text{\bf NU convine, b - cifra}[/tex]
Din cazurile analizate [tex]\bf \overline{ab}\in\{14,48\}[/tex]