Question

2|√48-2√2|+5|√12-√2|-3|3√2-√75|​

Answer 1

Răspuns:

• - 3√3 - 5√2

Explicație pas cu pas:

|√48-2√2| = I4√3 - 2√2I = 4√3 - 2√2 ( > 0)

I√12 - √2I = I2√3 - √2I = 2√3 - √2   ( > 0)

I3√2 - √75I = I3√2 - 5√3I = 5√3 - 3√2   ( < 0)

2|√48-2√2| + 5|√12-√2| - 3|3√2-√75|​ =

2(4√3 - 2√2) + 5(2√3 - √2) - 3(5√3 - 3√2) =

8√3 - 4√2 + 10√3 - 10√2 - 15√3 + 9√2 =

- 3√3 - 5√2

Answer 2

$2\sqrt2=\sqrt{2^2\cdot2}=\sqrt{8};\ \ \ \sqrt{48} > \sqrt8 \Rightarrow \sqrt{48}-\sqrt8 > 0\Rightarrow |\sqrt{48}-2\sqrt2|=\sqrt{48}-2\sqrt2\\ \\ \sqrt{12} > \sqrt2 \Rightarrow \sqrt{12}-\sqrt2 > 0 \Rightarrow |\sqrt{12}-\sqrt2|=\sqrt12-\sqrt2\\ \\ \sqrt{75}=\sqrt{25\cdot3}=5\sqrt3 > 3\sqrt2 \Rightarrow 0 > 3\sqrt2-\sqrt{75} \Rightarrow |3\sqrt2-\sqrt{75}|=-3\sqrt2+\sqrt{75}$

Expresia  devine:

$\it 2(\sqrt{48}-2\sqrt2)+5(\sqrt{12}-\sqrt2)-3(-3\sqrt2+\sqrt{75})=\\ \\ \\ =2(4\sqrt3-2\sqrt2)+5(2\sqrt3-\sqrt2)-3(-3\sqrt2+5\sqrt3)=\\ \\ \\ =8\sqrt3-4\sqrt2+10\sqrt3-5\sqrt2+9\sqrt2-15\sqrt3=3\sqrt3$