Question

Să se calculeze:
[(/2+/5)^2] ;
[(/5+/6)^2]
/=radical​

Answer 1

$\left(\sqrt{2}+\sqrt{5}\right)^2 = \left(\sqrt{2}\right)^2 + 2\cdot \sqrt{2}\cdot \sqrt{5}+\left(\sqrt{5}\right)^2 =2 + 2\cdot \sqrt{2\cdot 5} + 5 =$

$= 2 + 2\sqrt{10} + 5 =2+5+2\sqrt{10} = \boxed{7+2\sqrt{10}}$

$\left(\sqrt{5}+\sqrt{6}\right)^2 = \left(\sqrt{5}\right)^2 + 2\cdot \sqrt{5}\cdot \sqrt{6}+\left(\sqrt{6}\right)^2 =5 + 2\cdot \sqrt{5\cdot 6} + 6 =$

$= 5 + 2\sqrt{30}+6 = 5+6+2\sqrt{30} = \boxed{11+2\sqrt{30}}$

Answer 2

Răspuns:

$\bf (\sqrt{2} +\sqrt{5} )^2=(\sqrt{2} )^2+2 \cdot \sqrt{2} \cdot \sqrt{5} +(\sqrt{5} )^2=2 + 2\sqrt{10} +5 = \red{\boxed{\bf 7+ 2\sqrt{10} }}$

$\bf (\sqrt{5} + \sqrt{6} )^2=(\sqrt{5} )^2+2 \cdot \sqrt{5} \cdot \sqrt{6} + (\sqrt{6})^2 = 5 + 2\sqrt{30} +6=\red{\boxed{\bf 11+2\sqrt{30} }}$

Explicație pas cu pas:

Folosim formula:

$\red{\boxed{\bf (a+b)^2=a^2+2ab+b^2}}$